Carter in 76 was perceived as a moderate conservative in the South and carried the entire South. However, after governing as a liberal for 4 yrs his true colors came out and i believe he lost the entire South outside his native Georgia.
That's the way it appears when you just look at the Electoral map. Carter won all the South except Va. and Okla. in '76, yet retained only Maryland, DC, WV (which you maybe don't include under South, not everybody does) and Ga. there in 1980.
However, when you look at the swings involved the story looks quite different. All but five Southern states actually had underaverage swings away from Carter in 1980. It's just that he scored a number of close victories there in '76 and Reagan did the same in '80.
The five states are Georgia, Florida, Arkansas, Oklahoma and Texas. And Carter's 1976 results in Georgia and Arkansas were extremely high, very much unlike elsewhere in the South.