The Southern States played a small role in the slave trade..the majority went to the islands and Brazil on Yankee ships. It was a Southern President who banned the trans Atlantic slave trade to the US.
It was a U.S. Congress that did that. In the House the vote was 60 for and 49 against. Virtually none of the votes in favor of the end of slave imports came from representatives from slave-holding states. In the Senate the vote was 18 to 8. Many Southern senators didn't vote on the measure, possibly in protest. It might be more accurate to say that slave imports were ended in spite of Southern leaders rather than because of them.