Which Southern state has the highest number of black and white interacial couples?
Sociologically, that is an interesting question, but I don't think it can be answered the way you are asking it. What defines a "couple?" The way that some people date and break up it would be impossible to get accurate data on how many inter-racial couples there were.
Does that mean we can't at least get an idea? Well, the US census department keeps records on this sort of thing (for whatever reason). What we can check with them is "which state had the highest percentage of married people of different races?" The caveat to this is that the last census was in 2000, so the data might be a little outdated. I know you are asking specifically about black/white couples, but data on minority couples was the best I could find.
Drum roll, please....
The state with the highest percentage of inter-racial married people is Hawaii with 34.7%. Alaska and California round out the top. But you are asking specifically about the South. In that case, the answer is Oklahoma, considered West South Central, at 14.8 (one of the highest in the country!) Texas is next highest at 6.8%.
The state with the lowest is West Virginia with a 1.8%. Mississippi, Maine, and Iowa round out the bottom. Overall, the West has the most and the Midwest has the least.
Hope this helped!