How do you deal with votes and Blacks? Not about letting them vote of course, as I doubt that would happen easily, but how many they counted for when it came to Congress and presidential elections. Before the Civil War the 3/5 Compromise gave swarms of extra Representstives to the South, and after the war and when Reconstruction was canceled, they got a full 5/5ths from them.
IOTL the draft CSA Constitution maintained the 3/5ths clause. All the Confederates did was replace the euphemistic "all other persons" with what it really meant: slaves. I've read some speculation that it might have had to do with a desire to balance out representation between states with greater / lesser populations of slaves, but I suspect far less actual thought was applied to the clause's construction.
Really, the CSA's draft Constitution is one of the best living arguments against "states' rights" having been the South's main cause; states gain few rights (rights to reject a limited number of federal appointees and start little trade wars with each other) and actually lose one major right -- the right to restrict or abolish slavery. The vast majority of the rest of it is just a carbon copy of the U.S. Constitution that was supposedly so tyrannical.