I think we would have to rely on Buchanan not getting re-elected. He had a very defeatist attitude on the secession of the South, and sort of... let it happen, which had negative impacts when it comes to the Californian Secession that happened but decades after the Southern Secession Crisis.
Best chance would be to have a more radical candidate win the election (which, honestly, isn't that hard. Anyone would be more radical than Buchanan), and have them declare the Southern Secession Crisis as unconstitutional, and recognize them as separatists. This would lead to a Civil War, obviously.
I guess if that's too much of a push, avoid the economic crises that hit the USA around the time that the Confederate States shattered. They would've been able to scoop 'em up, declare a couple Black States to seal the votes, and then work on reconstructing Southern society.