My ATLs have seen such parties as the Democrats, the Dixiecrats (probably a spliter group), the Constitutionalists, the Conservatives and the Radicals.
Like Tom_B I think the anti-slavery movement will begin within the individual states and most likely the border states first. However, the Confederate Constitution does provide that a constitutional convention can be called by a set minimum of states. Its possible that slavery may be constitutional done away with.
However, I think it likely that some move towards a stronger central government would occur starting in the 1880s, once a 'new generation' of politicians have come to office.
I also think it likely that Texas will eventually flirt with independence its racial composition has it looking more West and Southwestward than the Deep South. It is also the only real 'frontier' state the Confederacy has (not bothering to consider Missouri) and that will influence its views.
In my ATL the Radicals, aka the Radical Rebels, are for a stronger central government and abolishment of slavery. They just may polymorph into the Conservative Party by the mid-20th century, I haven't quite figured that out yet.