There are a few different answers to your question, the first of which is counter-intuitive and important for getting to the second. Also before digging in, fair warning that since the defense of slavery and the defense of the slave trade are as closely intertwined, just as attacks on both are, it's hard to find a clear case of just defending trade rather than a general defense of slavery. Particularly so in the early United States where the slavery debate effectively is the slave trade debate.

The trade in slaves from Africa to the Americas, the Atlantic slave trade, stretches back nearly to the dawn of the Columbian Exchange. It's massive and horrifying, displacing millions of people stolen from their homes and families, subjected to a passage where many died, and radically transforming Africa, the Americas, and Europe. We might expect such a leviathan to generate opposition immediately, but it doesn't appear to have done so. As such, defenses were few. You don't need to defend something that no one is attacking.

In saying there was no opposition, I must stress that I don't mean everyone was a-ok with being enslaved. The history of slavery is full of examples of often inspiring, often horrific, often both at once resistance by the enslaved. The slaves were not, to any significant degree, thrilled with their lot in life and did what they could to escape it or push back at its edges to assert their own agency and reclaim parts of their lives. This is huge in understanding enslaved people and enslavers alike. But resistance to being enslaved is not necessarily the same as opposition to slavery. That's true even for famous slave revolts, like Spartacus'. They were against their being enslaved and their personal mistreatment, not against slavery in the abstract or in principle. When even the people afflicted don't often take a generalized stance against it, it's unlikely that people who understand themselves as of a piece with those doing the enslaving are going to do so. I wouldn't say that no one ever came to such a position, but not enough people did so to become conspicuous in the historical record and generate a response. Exploiting the labor of one's inferiors has probably gone on for as long as laboring for others has. Slavery was just a variation, if an especially cruel and extensive one, on the theme.

Until about the time of the American Revolution. I also want to stress that in saying that I don't mean to claim antislavery as a unique invention of Americans. Antislavery activism, which is initially concerned specifically with ending the Atlantic slave trade in the hopes that that will bring slavery to a gradual end on its own, arises on both sides of the Atlantic at roughly the same time. Revolutionary rhetoric in the nascent United States is a part of the story, particularly insofar as it's concerned with universal human rights, but that rhetoric is a product of the same intellectual trends operating elsewhere. David Brion Davis's Inhuman Bondage credits Enlightenment thought in France, England, and Scotland as well as then-new modes of revivalist religion with an emphasis on everyone's individual ability to attain salvation as contributing factors.

You asked about the American slave trade, which brings us to here. Before the Revolution there's quite a lot of trade but it doesn't require much defense. Afterwards, it begins to require more. So for the purposes of the rest of this, I'll take "American slave trade" to mean narrowly the business of importing slaves to the United States from Africa. (There's also a trade in which Americans participated as carriers, both in real terms and with the American flag as one of convenience, which brought enslaved people to the Caribbean and South America.)

Thomas Jefferson wrote a condemnation of the slave trade into the Declaration of Independence:

He has waged cruel war against human nature itself, violating its most sacred rights of life and liberty in the persons of a distant people who never offended him, captivating & carrying them into slavery in another hemisphere or to incur miserable death in their transportation thither. This piratical warfare, the opprobrium of infidel powers, is the warfare of the Christian King of Great Britain. Determined to keep open a market where Men should be bought & sold, he has prostituted his negative for suppressing every legislative attempt to prohibit or restrain this execrable commerce. And that this assemblage of horrors might want no fact of distinguished die, he is now exciting those very people to rise in arms among us, and to purchase that liberty of which he has deprived them, by murdering the people on whom he has obtruded them: thus paying off former crimes committed again the Liberties of one people, with crimes which he urges them to commit against the lives of another.[1]

It was cut and replaced by the passage accusing George III of fomenting slave revolts, which Jefferson blamed on northern slave traders (lots of New Englanders, particularly in Rhode Island, owned or invested in slavers) and South Carolina and Georgia. I'm not familiar with the debates in Philadelphia over the passage, so I can't say if they had anything interesting to say in the trade's defense or not at the time.

For that let's skip ahead a few years, but not leave town just yet. During the Revolution, the Atlantic slave trade is cut off. The rebelling colonies chose to suspend the trade during the war. By the time the Constitution was written, there was a general -though by no means universal- consensus that the Atlantic trade was horrible and ought to be ended. Doing so is also, as aforementioned, the signature policy of the antislavery movement.

The Constitutional convention thought about giving Congress a sweeping power to regulate commerce. Supporters include Virginia, for reasons that will become important in a paragraph or two. The Lower South (Carolinas and Georgia at this point) object strongly. If Congress has that power, then it can outlaw the Atlantic slave trade and essentially ruin them. Unless they get some powerful surety that no such thing will happen, they're out. I regret that I don't have their remarks to quote, but what came of them is of great significance to what follows. The Congress gets its power to regulate commerce, but that general power has two limits upon it. The first is the most famous: Congress cannot outlaw the slave trade until 1808, twenty years thence. That's at least twenty years of slave imports. Nothing in the Constitution requires the nation to outlaw importing slaves at that or any future date; it just becomes an option. This provision is then made un-amendable, placing it coequal with equal representation of states in the Senate. That's a pretty huge deal.

But here's what the clause says in full:

The Migration or Importation of such Persons as any of the States now existing shall think proper to admit shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a Tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.

The tax portion is almost always forgotten, but it wasn't at the time. Let's go up to New York. It's March 14, 1789. George Washington has been president for fifteen days. A fellow Virginian veteran rises in the House of Representatives, Josiah Parker. The House is considering import duties and hey, here's an import duty that the Constitution tells them right there in plain English that they can levy. Parker suggests amending the bill to put in the full ten dollar amount. They were already talking about taxing china, crockery, gunpowder, mirrors and brushes. Why not people too?

You can't argue that this is somehow unconstitutional. Arguments that things the Constitution permits in black and white are unconstitutional don't get really popular for a decade or two yet. But opposition comes all the same. There are procedural arguments over how Parker's idea isn't proper to put on a general tariff bill, but rather should go on its own. He later withdraws the amendment and agrees to submit it separately, but that doesn't mollify the real foes.

It shouldn't have, really. Parker made no secret of what this was all about. His reasoning is in the Annals of Congress:

He was sorry that the constitution prevented Congress from prohibiting the importation altogether; he thought it a defect in that instrument that it allowed of such a practice; it was contrary to the Revolution principles, and ought not to be permitted; but as he could not do all the good he desired, he was willing to do what lay in his power. He hoped such a duty as he moved for would prevent, in some degree, this irrational and inhuman traffic

(Back in a moment with the rest.)