Apologies for the bump, but I was just discussing this topic a few days ago so I actually have the number on hand.
https://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1295&=&context=student_scholarship&=&seiThis paper talks about how Eisenhower overperformed among Black Voters in 1956, but more importantly for our purposes, it cites Samuel Lubell as saying:
Reporter Richard Lyons of The Washington Post concluded that, in all the cities they studied, Ike won a greater percentage of the black vote than he did in 1952. The biggest impact of the Negro switch was felt in the South. In some northern cities the change was “hardly measurable” and the “overriding issue was civil rights.” African Americans switched in far greater numbers in the South because southern Democrats were opposed to civil rights, whereas in the North they were generally for it. Lyons argued that “Negroes can take credit for holding Tennessee for President Eisenhower. Their switches in Memphis alone were far more than his statewide margin.” Samuel Lubell concluded that “in the northern cities Eisenhower’s gain over 1952 was 8 percent while in the South the same Southern Negro wards and precincts which gave Eisenhower 19 percent of their vote in 1952 gave him 47 per cent in 1956.”
Unfortunately, it doesn't say how well Stevenson did among Southern Blacks in 1956, but given the very low third party share at that election (South Carolina exempted, and in South Carolina the Third Party Voters were staunch segregationists so not a very black demographic) I am pretty sure Stevenson won Southern Blacks, even in 1956, and that was
after winning them handily in 1952 with a segregationist running mate, and even in 1956 he would have won them handily nationwide. Just goes to show you the absurd strength of the New Deal Coalition I guess.