I've often thought about if there's any way to make the premise of the movie White Man's Burden, which has a majority black U.S. with a white underclass, plausible. I think it could just barely happen, but I'd be interested to hear the ideas of others.
Here's the limitations.
1. The POD doesn't have to be after 1776, but the state needs to be derived from British colonies and called "The United States of America"
2. While it doesn't need to be as large as the modern U.S., it can't contain only OTL's South. It must at minimum contain some of the Mid-Atlantic states. It can contain bits of the Caribbean and Latin America if you wish, but they should be a distinct minority in terms of population and land area.
Any hot ideas?