I think Liberia was supposed to be America's version of a Bantustan (albeit different timeframe). White Americans didn't want to part with any of "their own land," nor did they need to pay lip service to native sovereignty like in South Africa because black people are the majority there, while they are a minority in the United States. So I don't think it's likely that Americans would part with any of the continental US to make a homeland, even the black dominated parts of the Mississippi Delta IMO. It could be possible however for a Bantustan to be created in the Caribbean, in an ATL where the Teller Amendment isn't passed and the US annexes Cuba.
Having said that, segregation and apartheid were already pretty much the same OTL in terms of how much they restricted black people. For starters, segregation and "apartness" mean pretty much the same thing, and they were viewed as near identical structures by contemporary pan-Africanists. If you go to the apartheid museum in Johannesburg you can see benches that say "For Europeans Only," similar to pictures I have seen of water fountains labeled "Whites Only." The major difference IMO is the apartheid government paid lip service to the concept of black sovereignty by creating "independent" bantustans with black political leaders (puppets, but still) while segregation-era US didn't even do that.