What I was going to say.
That being said, would CSA superhero (or at least on of them) be a a super-cowboy like the Lone Ranger or something? That is how I (a non-American) would imagine it.
It really depends what part of the South you're talking about. Texas is really the only ex-Confederate area where cowboys are a major aspect of local culture, and both Texas and the rest of the South view each other as significantly different. To take one small example with
major cultural significance, the type of meat used in barbecue is different; the Carolinas and Memphis (along with most of the rest of the South) associate barbecue specifically with pork, whereas Texas uses beef.
OTL, the 1860's Confederacy was (obviously) more planter-class dominated, with the population concentrated in the East and Upper South. Texas was comparatively insignificant, as was Florida (today the two most populous states in the former Confederacy). How the demographics change would probably affect the degree to which Texan culture dominates, or whether it becomes another regional flavor within the broader Confederate culture. And note that there would be less of an experience of westward expansion, as the Confederacy would presumably be contained within its original boundaries, so cowboys might be less of a part of the general cultural mix in general.
You could end up with a Texas Lone Ranger-esque hero, but you could also end up with a Batman or Superman-esque character roaming the streets of Richmond or New Orleans, fighting crime in the city. The latter would be more likely if the East remains the center of gravity.
Depending on developments, the traditional background could be rich planter's son using his inherited fortune to fight crime (a la Bruce Wayne or Tony Stark), or a humble farmboy upholding traditional values (a la Clark Kent). Swamps (of which the South had, and to some extend still has, plenty) could be settings for spookier atmospheres.
Since several people have mentioned the KKK, I should point out that it's a post-Civil War phenomenon, so it wouldn't exist (lynchings, etc. obviously still would).
Rogue galleries would be interesting (if somewhat frightening) to imagine. Like OTL, they'd probably be shaped by the cultural and political fears of the era, so you could imagine sinister Yankee agitators, Communist infiltrators, slave rebels (I'm now imagining a voodoo-zombified Nat Turner) later evolving into black militants (a Black Panther-esque character would definitely be a villain in Confederate comics). If the CSA involved itself in global politics, you could imagine whatever its enemies were showing up as well (Czarist spies, anyone?).
