Birth of a Nation, Gone with the Wind (except it ends "happily" with the Old South "free" from Northern "opression"); basically all your "lost cause" type of films.
Birth Of A Nation is an interesting case, because it's actually pro-Union, or at least pro-Lincoln, suggesting that he was the protector of southern whites against the depredations of the(unnamed but certainly implied) Radical Republicans.
If I'm remembering it correctly, the overall message of the film is something like "Yeah, okay, the South shouldn't have tried to secede, but now that that's settled, the North needs to butt out of their affairs and let them deal with the colored race the way as they see fit". Even the very title of the film suggests that what needs to happen now is unity(albeit on terms very much favourable to the white South).
So, in a surviving CSA, Birth Of A Nation would be about the birth of the
Confederate nation, with no weepy homages to Lincoln, and every Republican made out to be a Radical.