While the Civil Rights Act, as well as the urbanization and rise white collar employment in the region, began the transition of the South from the Democratic party to the Republican party, it really took until the 90's for the South to go solid red. Before that, even as the South gradually transitioned to voting Republican nationally, local elections were still very Democratic for quite some time, and I believe it took until the "Republican Revolution" of 1994 for that to really change.
So the challenge is to keep the South Democratic with a POD no earlier than the passage of the Civil Rights Act of 1964. No cheating and just having Civil Rights not happen. Keep in mind Democratic doesn't mean Socially Liberal Democratic, it just means within the Democratic party.