I would say 1960 as well. The black Protestant church, which was the most influential institution in black America at that time, was filled with Protestant ministers who disliked Kennedy’s Catholicism. This also included Martin Luther King Sr. Also...Kennedy didnt have a strong Civil Rights record when he ran in 1960:
Kennedy offered no strong civil rights record, as most biographers have noted. In the wake of his failed bid for the vice presidential nomination at the 1956 Democratic National Convention, Kennedy in fact strove to bolster his standing among powerful southern Democrats by steering a ruthlessly political course, seeking, in the words of Robert Dallek, “a strategy for accommodating all factions of the Democrat party on civil rights.” Doing so left Kennedy at best equivocating on the 1957 civil rights bill, at worst pandering to his party’s most extreme segregationist elements. His meetings and alliances with segregationist southerners, including a breakfast meeting with Gov. John Patterson of Alabama and the president of the Alabama White Citizens Council Sam Englehardt, made most black voters wary of his civil rights commitment. His naming the southern Democrat Lyndon Johnson as his running mate raised more suspicions.
http://archive.oah.org/special-issues/teaching/2008_12/article.pdf
But how many black people were actually voting in those precincts in 1960? voter suppression was rampant back then.
Somewhere around 30% of blacks were registered to vote in GA pre 1965 VRA