Don’t You Weep, Don’t You Moan by Richard Coleman, a 1955 paperback edition shown here. I don’t know if it’s really “A novel of raw desire”. Originally published in 1935 and garnering good reviews at that time, even at the New York Times Book Review (still out there online), it might be called a torrid soap opera with literary leanings and set in Charleston, South Carolina’s African-American community.
I assume the title’s a nod to the old spiritual, which was also turned into a folk song by Pete Seeger (“…Oh Mary, don’t you weep, tell Martha not to moan”). I don’t know the artist on this one, and couldn’t even trace it on a reliable go-to site like pulpcovers.com, but the illustration is handsome.