There have been many Reconstruction threads here, and the consensus seems to be that, unless radically changed, it was unsustainable once the federal government got tired of occupying the South. But what about the period immediately after, from the mid-1870s to the early 1890s?
At that point, Redeemer governments were in power throughout the South, but African-Americans were still on the voting rolls. In some Southern states, more black candidates were elected to office in the 1880s than the 1870s, and there were districts like North Carolina's "Black Second" that reliably sent African-Americans to Congress. There was a rising black middle class in the lowland Carolinas, Savannah, Mobile.
Could an equilibrium have been maintained _there_, or were race relations destined to fall to the nadir?
I'm uncertain, but I'd expect that the answer would have a lot to do with the fortunes of populism. The Virginia Readjusters of the 1880s and the North Carolina Republican-Populist coalition of 1894-98 came in with the support of black voters, and once the Bourbons got back into power, the first thing they did was disenfranchise the African-Americans. So what we might need is either the Bourbons co-opting the Populists early on, meaning that black voting rights aren't seen to be a threat to their power, or else the Populists taking power _and keeping it_. Better results in the early Supreme Court civil rights cases also wouldn't hurt, but I suspect the main factor would have to be practical state-level politics.
Finally, if this can be done, what happens next? Things weren't as bad in the 1880s as they would get later on, but they weren't peaches and cream either. There would still be segregation and lynching; there would probably still be convict leasing. TTL would still need a civil rights movement; where and when would it get started?