Looking at data on who black voters have supported in past presidential primaries (starting with 1980), it appears that they generally prefer establishment Democrats; unless the most establishment candidate faces a challenge from a viable black candidate (Barack Obama) or black candidate who’s remotely taken seriously (Jesse Jackson). Or Ted Kennedy, apparently.
Um, do we know how black voters voted in the 1980 democratic primaries? Did they back Kennedy?
According to the exit polls, yeah, but with a fairly modest majority (55%). Carter’s firing of Andrew Young caused some controversy.
Carter won every county in the Black Belt and won Baltimore and Detroit. Kennedy won Philadelphia, Cleveland, and all five NYC boroughs. It's tough to really tell without precinct data.