There have been a few Louisiana gerrymander proposals with black-majority districts:
Stephen Wolf's 3-3 and 3-2-1 maps
twohundredseventy's 3-3 map with 3 black majority districts
shock27's similar but lower AA %s map
While those are impressive, one thing that is missing is a 4-2 map. Yes, overall the VRA helps both minority representation and Dems to have at least one seat in most Southern states, but this is still an interesting thought experiment.
There are a few cases of water contiguity, but all districts are fully contiguous.
While a 53/54% 08 Obama district would be a tossup in most of the country, in South, it's somewhere between a Lean and Likely D. The "Dem" number is the average of all federal results in 2008.
Without further ado...
54.0% Obama, 58.5% Dem
45.3% W, 49.0% B
53.5% Obama, 56.4% Dem
47.3% W, 46.7% B
14.9% Obama, 22.4% Dem
87.0% W
15.8% Obama, 25.4% Dem
86.0% W
53.4% Obama, 58.1% Dem
50.8% W, 39.6% B
53.2% Obama, 57.2% Dem
45.7% W, 41.0% B