This could be interesting.
Lessee... For the following decade or two after the brutal ACW ends with a nasty stalemate/victory, economically and politically isolated CSA faces economic turmoil, motivating many white Southerners --low to middle income farmers and other professions that don't rely on large-scale slavery to function-- to emigrate to either the United States or elsewhere. (Maybe you get a contingent of CSA expats in Argentina or even Canada, those are colorful details.)
After all, the Europeans decided to rely on Plan B: cotton from Egypt, cotton from India, cotton from everywhere else except for the politically poisonous "slave-ocracy" of the CSA.
With the war over, some of the propoganda from the north is seeping in for some: non-wealthy Southern whites begin to see their economy as based on obsolete practices. Within ten to twenty years, thousands of these people get out while the getting is relatively good. There's plenty of space to start fresh with in the western USA, and Spanish isn't so difficult to learn as many emigrants discover. By the turn of the century, in South America, there are plenty of ex-Confederate farmers and factory-managers to be seen.
The trend of lower and middle income whites emigrating is self-sustaining: Rich owners of large plantations end up buying smaller properties to append to their own/expand operations. (This accelerates the consolidation of the vast majority of wealth
belonging to the large-scale slave-owning planation-owners.) Enough folks are still buying CSA cotton --on the downlow or otherwise-- to make this worth their while.
With more and more white workers voting with their feet, some CSA pro-slavery enthusiasts, "on principle," re-open the slave trade. This is not impossible, what with West African infrastructure for slavery
very much in place in the late 19th century.
Lessee... Fewer whites, more people brought into slavery...
More plantations perhaps relying on some "trustee" slaves to help with stock-counting and transit and what-not...
All you'd need is a Nat Turner to show up with an aggressively abridged Das Kapital to stoke up some sparks.
Or so I speculate.