They would have been an international outcast had they allowed/supported the international slave trade. Great Britain banned the trade in 1808 (same year the US banned the import of slaves) and actively began a blockade of Africa to suppress the trade (initially only on British ships, but later on ships flying any flag). The US joined in in this effort in 1819 and the two states began working together in 1842 with the Webster-Ashburton Treaty. France banned the slave trade in 1818.

A major goal of the CSA was to gain international recognition and support, especially from strong states like Britain and France. The slave trade, by the time of the southern rebellion, was seen as particularly abhorrent (slavery was basically seen as abhorrent as well, but was more recently outlawed in most states than the slave trade; it was also the raison d'etre of the CSA so banning it wouldn't have made sense at the outset of the war), so if the CSA legalized it, it would have ostracized itself.

Further, because basically all other states outlawed it, the CSA would have had to have worked with pirates or transported the slaves from Africa by itself. Both of these options were unsavory as working with pirates would have even further ostracized the CSA internationally and it had no means to ferry slaves itself.

Overall, the CSA basically had no choice. If it had legalized the slave trade, it would have basically accepted that Britain and France would not recognize or support it (unless it won the war), which would have basically been the CSA accepting loss at the outset.

See Abolition: A History of Slavery and Antislavery by Drescher for more

There are a few important reasons that the CSA outlawed importing slaves, despite the interest of a few extreme radicals resuming direct trade with Africa. The first is that by the nineteenth century, white Americans have a lot of squeamishness about the trans-Atlantic slave trade. Part of domesticating slavery at home to the point where they could feel ambivalent-to-good about it on its "merits" was outsourcing the cruelty to the slave ships. (This was much easier than actually treating the slaves better, though enslaved Americans do benefit from a general reduction in brutality taking place contemporaneously. In the nineteenth century slaves are mutilated, burned alive, and such more rarely than before.) What happened on them in the Middle Passage was so grisly that enslavers could welcome the comparison and flatter themselves as humanitarians, rather than tyrants without scruple.

Enlightened sentiment only gets one so far, though. One also has to consider period ideas about Africans, which are not enlightened by any reasonable measure. Enslavers, as a rule, don't have a high opinion of black Americans. But black Americans speak English, are probably Christians of some sort (often Methodists or Baptists), and behave in a manner largely familiar to their white enslavers. All the fears of what they really think and would really do if they had half the chance, namely giving white Americans what their own history logically dictated they had coming many times over, still apply but they apply in a way that white Americans are used to. People freshly imported from Africa will probably not speak English, be Christians, or otherwise adhere to any form of nineteenth century norms to which their white enslavers are accustomed. They're consequently much more threatening, raising the specter of cannibalism and other horrors much more readily. When insurrection conspiracies, or rumored conspiracies, are uncovered anything that looks like a traditional African religious practice is singularly frightful to white Americans. The ability of enslaved conjurers wise in African traditions to act as leaders of the enslaved, and to pull other slaves more culturally in that direction, is an extension and exacerbation of he threat posed by black religious leaders (and more broadly any black leadership) in general.

We can go lower still; there are brute economic concerns involved. The biggest of these is that the Confederacy at the time of their constitutional convention is just six cotton states. (Texas comes along a little bit later because Sam Houston deliberately slow-walked secession.) Those six cotton states are thriving economically, but they have structural problems that make their viability as an independent nation questionable. More troubling still, the Upper South states (which mainly have tobacco, hemp, and wheat as their staple slave-grown crops, plus one other vital concern we'll get to shortly) have not joined the rush out of the Union. They Confederates don't know this at the time (March 11, 1861), but the Upper South will initially vote against joining their rebellion. They're keen enough to prevent that that they dispatch secession commissioners to lobby the still-loyal slave states.

The Upper South can't contribute cotton to the Confederacy. I can't summarize it better than James McPherson does, so here goes:

These eight states [the Upper South] contained most of the South's resources for waging war: more than half of its population, two-thirds of its white population, three-quarters of its industrial capacity, half of its horses and mules, three-fifths of its livestock and food crops.

If it came to war, and the Confederates expected some kind of armed clash, they would be in a far stronger position if they had those things all on hand. Getting them required appealing to the Upper South in every way they could manage and one of those ways was to ensure no new slave imports. That's because the Upper South's most vital product, from the POV of Lower South whites keen on their region's prosperity since the 1790s, is people. The Lower South is more, proportionately, enslaved but it has fewer slaves and (excepting the East Coast) less overall agricultural development. The Upper South, because the tobacco market took a beating in the late eighteenth century and never really recovered, has more slaves on hand than the whites can profitably use. So for all those decades, it's been selling its surplus down into the Cotton Kingdom to the tune of a million people in a massive forced migration.

This is a win-win for the whites involved. The Lower South has the standard New World white problem if too much stolen land and not enough labor to exploit it all. It's by no means all wilderness below North Carolina and Tennessee, but things do get wilder and less steadily cultivated as one goes inland and westward. By the late antebellum, the big growth regions are along the Mississippi Delta and in Texas but there's still room to expand almost everywhere except South Carolina. They need those enslaved people as the engine to turn misery into cash.

The white Upper South, by contrast, is drowning in surplus slaves it doesn't need and constantly fears being eclipsed by them...even if this is more a demographic problem in the Lower South. The shift from tobacco to more diverse crops reduced labor needs and "idle" blacks are seen as a kind of existential threat in waiting. Who knows what they'll do? They might revolt. Some did revolt. The growing population of free blacks, largely the result of a flush of manumission and emancipation just after the Revolution, is troubling for all the same reasons. So it's possible for Upper South whites to hope they can slowly drain away their excess black population into the Lower South, leading to the dream of a lily white future free from the insecurity of living in a slave society...at a nice profit. The last point is important; when tobacco rebounds a bit in the 1850s the direction of slave sales partially reverses. It's the combination of too many enslaved people to be profitable for the enslavers and the market elsewhere that animates the dream of whitening the Chesapeake and the south bank of the Ohio. In the grotesque logic of slavery, human beings are a central Upper South export item.

By keeping the prohibition, the Lower South essentially promises the Upper that everything can continue as it has. They're want to keep consuming Upper South enslaved people for the foreseeable future, not subject their enslaving suppliers to competition with fresh African imports that might drive down prices even though that might be in the economic interest of the cotton states. This isn't the decisive point that drives the Upper South (bar four states) into the Confederacy, or they would have gone on ratification of the Confederate Constitution, but it was a vital concern for enticing them in the minds of the Lower South authors of the document.

Sources

Prelude to Civil War and Road to Disunion (2 vols, esp 2) by William Freehling

Roll, Jordan, Roll by Eugene Genovese

River of Dark Dreams and Soul By Soul by Walter Johnson

Battle Cry of Freedom by James McPherson

Update: This post previously said "a few million" enslaved people were forcibly moved into the Lower South. The actual number is closer to one million, as I was reminded when re-checking my sources. I've fixed it in the original text.

Follow up question: the other two differences mentioned are often floated around as theoretical reforms to the constitution. How long have these two reforms been around, considering the confederacy thought they should be added?

1. They banned the international slave trade from everywhere except the US slave states and territories in an attempt to get more states and territories to secede by showing a sort of kinship with them.

2. The Confederacy could also ban the trade from particular members of the aforementioned accordingly if adversarial attitudes were shown against the Confederacy.

3. The importation of slaves from elsewhere was banned as to keep the prices of slaves up instead of dealing with foreign competition that would drive prices down; protectionism.

4. The differences between the two constitutions goes beyond what you listed. The President could also fire cabinet members at will and any other civil servant with reason. They also had more power over the purse than the US President at the time would have. The Confederate Congress had to limit all bills to one topic only (no omnibus or riders or earmarks), most federal spending had to be explicitly approved by Congress in specific dollar amounts, and they couldn't spend federal money from some states on internal improvements in other states (except for waterway navigation improvements), as what was happening with the US federal government spending tax dollars from Southerners on Northern states without their consent.

They also couldn't do tariffs designed to protect certain industries over others. The Confederacy levied a 15% tariff on ALL imported goods unlike in the US where tariffs had varying rates and only applied to certain goods as to protect only certain industries. It was also easier to amend the Confederate Constitution, only requiring 3 states to approve proposals and 2/3 of states to ratify it, Congress did not need to ratify amendment unlike how in the US 3/4 of states have to approve, 2/3 of states to propose OR 2/3 of both houses of Congress approve of the proposal.

States could also impeach some federal officials in their states, make agreements with other states concerning waterways (with approval from the federal Congress), and could even levy taxes on ships using their waterways while the federal government could collect the surplus revenue from state taxes on tonnage (with congressional approval) except for seagoing vessels or other water improvements (without Congressional approval). States could emit their own bills of credit too.

The 2nd amendment in the Confederate Constitution also read differently as two of the three commas in the original are removed so it reads more akin to how gun control people interpret it, of course they would do so as to make sure slaves or freedmen or anyone adversarial to Confederate society couldn't argue for gun rights. The Confederate Congress could also allow cabinet members to consult on the floor in decision making (not voting of course), something from the British parliamentary system not found in the US.

Oh yeah, and the Confederate Constitution acknowleges the states as soveriegn entities and is ordained by God, the meaning of permanent federal governemt simply comes from the provisional Confederate Constitution it was supposed to supersede, there's actually a lot of differences, the two constitutions are like half the same and half different, lol.

Source 1

Source 2

Those are really interesting details, thank you. This may be a question for another post (I can reask if you'd like), but could you describe the mechanism of this massive population shift? Were plantations buying individuals, or did they contract to bring down large numbers together? Were slaves transported individually, massed in the south and resold? I'm just trying to get my brain around the scale of what you're describing.