Whistling Past the Graveyard by Susan Crandall
Thinking that life has to be better with her mother, who left her when she was three, than with her overly strict grandmother, Starla runs away. Runs away from her grandmother, the bully that always gets her in trouble, her life of always wanting more. But when she is picked up by Eula, a black woman with a white baby, Starla needs all the grit she can muster to stay alive. With characters you feel you have known all your life, together with the drama of real life in the South in 1963, makes this story one to put on the top of your list.