I'm going to try and address your question within the context you specified to /u/cotton_eyed_bro below; if it's not what you're looking for, let me know and I'll try to refine my answer.
Your question appears to be rooted in the assumption that the transatlantic slave trade was thriving until shortly before the civil war; this is not the case, and if the source you were reading implies that, I'm afraid you've been a bit misled. The United States had abolished the importing of slaves by federal law in 1807 (taking effect in 1808); Britain, which was responsible for as much as 28% of all slave cargo shipped to the United States after independence, abolished the trade in its entirety in the same year. Estimates on the extent to which illicit trading in slaves continued after 1807 have varied considerably, but the trade to America appears to largely disappear after 1820.
In the years just before the onset of the Civil War then, the transatlantic slave trade was for our intents and purposes dead; it was very much a permanent situation by that time. So in order to answer your question, I'm going to have to push your time-frame back a few decades to the turn of the century.
Generally speaking, the United States was never particularly hungry for slaves from Africa compared to the colonial holdings of the European powers. Between 1776 and 1808, continental North America imported approximately 123,000 slaves; in the same period, the Caribbean imported more than 1,520,000. To put it another way, for every slave arriving in the United States in that period, 12 were arriving in the Caribbean; 7 of those in the British Caribbean. Whilst it is important to note that America also imported slaves from the West Indies - and thus some of those slaves recorded as being Caribbean-bound ultimately ended up being sent on to continental North America - in any given year the USA rarely imported slaves on a comparable scale to the European colonies. The questions that arise from your initial inquiry are, then, how and why did the US end the foreign trade in slaves so early, and was the south a participant in or an obstacle to that process?
The answer to the first part of that question lies in the American war for independence. In the 25 years preceding the Declaration of Independence, records indicate that continental North America imported an average of 5,850 African slaves per calendar year; in the 25 years immediately after, that figure plummets to just 1,400. During the course of the American revolution, every part of the infant nation either outlawed or suspended the slave trade - some for moral reasons, some for fear that the instability of the period would make it harder to prevent slave rebellions (which, the slave-owning community believed, were more likely to originate from African than colonial-born slaves) and others out of a desire to undermine or separate from the British economy.
The demand for fresh slave labour was still as strong as ever, however. In the absence of imports from the rest of the world, the USA began to develop a much stronger internal slave trade, redistributing its internal supply of slaves through market processes or relocation between states. Such trade had always existed and served to reduce the demand for foreign imports of slaves, but the closing of US ports to slave ships placed greater emphasis on its importance. From 1790 to 1860, around one million slaves were probably sold and moved through this internal market - probably more than double the number of Africans brought to continental North America in the 230 years slavery existed there. After the war, most states kept or only fleetingly lifted their bans on the slave trade; Georgia alone had permanently restored the trade by the 1787 Constitutional convention. Nonetheless, the planters of the Lower South as a whole felt importing slaves from abroad was a right to which they were entitled, and a means by which they could ensure the future of slavery in the long-term if the domestic trade became unsustainable or too costly. As a concession to them, the Constitution guaranteed states the right to import slaves until 1808 if they wanted to do so.
In 1805, with the constitutional protection for the trade about to expire, anti-trade representatives in Congress began to work towards securing abolition to take effect on the earliest possible date: January 1st, 1808. In these debates, the south's leaders and representatives divided. The Upper South and especially Virginia had developed a strong excess of slaves, and there were serious concerns about the implications of this among contemporaries for Virginian society and economy. In contrast, the Lower South - with its rapidly growing cotton industry always hungry for more labour - had a constant need for new slaves. It was this labour imbalance that had fuelled the growth of the internal slave trade already, with labour moving from the Upper to the Lower South when the international market could not provide enough. Furthermore, South Carolina had re-opened its ports to slave imports in 1803; this served as a phenomenal boost to the slave trade. In 1804 alone, the US imported more slaves than it had in the preceding seven years combined; most of these slaves were sold on beyond South Carolina, creating a rival source of new labour to the internal trade.
The moral climate of the wider US was also favourable to abolition - even among pro-slavery elements of society, the horrors of the slave trade were difficult to deny. Congress had repeatedly passed measures aimed at regulating and restricting the practicalities of the slave trade with mixed success; the mass imports to South Carolina after 1803 had highlighted the inadequacies of these measures and strengthened the case for federal abolition.
Ultimately, the slave trade could not survive; many in the Upper South had a vested interest in its demise to promote the domestic slave trade, many northern abolitionists hoped to end slavery altogether by choking off the supply of new slaves, and the planters of the Lower South could not make a convincing economic or moral argument for its retention.
In the final years of the trade, after South Carolina re-opened her ports to slaves and abolition of the trade approached, the US experienced an unprecedented burst in new slave imports. In 1807 alone, more than 35,000 slaves arrived from Africa in the United States - all in all, the years 1803 to 1808 account for nearly 65% of all known estimated slave imports in post-independence America. Around one in every six Africans taken directly to the USA as slaves from 1628 to 1860 - a period of 232 years - are thought to have arrived there in the final half-decade of the slave trade's legal existence. In other words, a period amounting to just 2% of slavery's existence accounted for 15 - 20% of all foreign slave imports.
This burst in imports at the last minute, a supply of labour sufficient to account for anywhere between 25 - 35 years of lost external trade, surely gave southern slavery the boost it would need to adapt to the total loss of the legal foreign slave trade. When the southern states seceded from the union, restoring the slave trade was not in their minds - indeed, the Confederate constitution prohibited the "importation of negroes of the African race from any foreign country", except for the USA, though there were certainly many in the south hotly opposed to this provision (and some who only accepted it for fear the Confederacy could not find international support without it).
In terms of the feasibility of restoring the transatlantic slave trade, that is difficult to say. The slave trade was in global decline at this point anyway, and after 1850 was predominantly the domain of the Spanish, who had only ever accounted for a tiny portion of shipments to North America. With the USA, Britain and France all prohibiting slavery, I imagine that the Confederacy would have had an enormously difficulty time meaningfully reinstating it. Though some certainly wanted to, it is likely that the southern US would have always been much more dependent upon continuing to trade internally rather than importing Africans.
TL;DR: The trade's abolition took place a long time before the civil war. The south came to rely on an internal market for slaves, whereby excess labour in the Upper South was sold on to the Lower South for profit. Though Lower South planters resisted a ban on the trade to try and keep labour costs down and the supply high, Upper South interests in promoting a domestic trade and northern anti-slavery interests restricted their capacity to resist the outlawing of slave imports from Africa. By the time of the Civil War, the south's prospects for restoring the trade even if they won were poor, and though some certainly wanted to, the Confederate Constitution did outlaw the trade.
Selected Bibliography
This is a good question, however, you should have written a title that is a tad bit more relevant. It is a great question, just remember that the people answering want a questions that are less specific. The slave trade was certainly effected by the civil war, that is unquestionable. Maybe you should try and ask how Buchanan's presidency altered the slave trade, or what the status of the slave trade was a decade prior to the civil war. This subbreddit contains many reputable sources, dont insult them with such a narrowly stated question. Though, I too would like to understand the current state of tge slave trade years prior to civil war.
Typing on cell phone......
Sorry, I know I definaltely seem rude. I know people can come off crass on this place. Life is scary....