MONTGOMERY, Ala. — In 1931, Alabama wanted to execute the black Scottsboro Boys because two white women claimed they were gang-raped. Now, state officials are trying to exonerate them in a famous case from the segregated South that some consider the beginning of the modern civil rights movement.

Two Democratic and two Republican legislators unveiled proposals Monday for the legislative session starting Tuesday. A resolution labels the Scottsboro Boys as “victims of a series of gross injustice” and declares them exonerated. A companion bill gives the state parole board the power to issue posthumous pardons....