I believe Stevenson supported civil rights in an abstract sense, but he did pick two segregationist running mates, when asked about the issue said "civil rights are not very important," and if I'm remembering correctly implied that he thought Eisenhower was going too far sending the National Guard to integrate schools.
While granted that Stevenson's first running mate John Sparkman was a segregationist, his second running mate Estes Kefauver refused to sign the Southern Manifesto of 1956 (along with Al Gore Sr. and Lyndon Johnson) and voted in favor of the 1957 and 1960 Civil Rights Acts. I do not know how Estes Kefauver would have voted on the 1964 Civil Rights Act had he lived past 1963 though.
