There hasn't been a black governor since Doug Wilder stepped down from the post in Virginia in 1994. Wilder, in fact, is the only African American ever to have been elected as governor.
Only one other African American has ever served as governor. In 1873, P.B.S. Pinchback, the lieutenant governor of Louisiana, was elevated to the post of acting governor for a grand total of 43 days.
(This fun fact comes courtesy of Governing States and Localities, our fine textbook.)