The CSA has won its independence, comprised the OTL CSA minus Tennessee.
In Confederate Elections, Jefferson Davis was a nonpartisan in the 1861 election and the two parties in the 1863 legislative election were the pro-administration and anti-administration parties. On the other hand, in the Virginia and Louisiana gubernatorial elections of 1863 the candidates were all Democrats.
Given the Planterocracy's opposition to industrialization, I think that'd be one split between two potential parties.
With freedom being so close, there'd likely be more pressure to conscript people into the slave patrols. Considering how Alexander Stephens considered enslaving poor whites, planters in general thought pretty lowly of the yeomen, and how sharecropping had already started in Mississippi for poor whites before the civil war, I think there'd be a lot of focus by Planters on promoting the sharecropping system (with certain financial interests coming along for the ride).
The Confederate Constitution banned the federal government from spending money on internal improvements for the purpose of promoting economic growth. However, the war created a need for industrialization and I think there'd be a work-around for infrastructure of it was military in nature. In essence, industrialists could cooperate with military-types to get their infrastructure goals through. Ergo, "this road we're building between two economic hubs has nothing to do with investing in the economy, it's about being able to move the troops around and supplies from point A to point B!"
Cajun interests might also come up as an issue.
So one party as a coalition of Defense, Industrialists, and Poor Whites vs another party of Planters and financiers?