There's a lot of activity this weekend as Black History Month begins.

* The Museum of American History, 14th Street and Constitution Avenue NW, sposors two free concerts focusing on the evolution of black music in this country. Saturday at 2, guitarist John Cephas and harmonica player Phil Wiggins perform tunes in the Piedmont blues tradition. Sunday at 3, the Chris Royal Quartet performs "Louis Armstrong and the Hot Five: The Emergence of the Jazz Soloist." The Saturday show is in the Hall of Musical Instruments on the third floor; the Sunday peformance is in the museum's Palm Court. 357-2700.

* Jarrett Beal (Martin Luther King's great nephew) plays the late civil rights leader in "The Boy King" at the Kennedy Center Saturday at 10:30 and 12:30, Sunday at 1. This family-oriented play portrays the boyhood life of King and is performed by Stage Directions of Atlanta. It's recommended you show up at least twenty minutes before showtime. The show is free and recommended for children in grades K-6. 254-3600.

* The folklore of Zaire and Central Africa comes to life in a free storytelling program at the Museum of African Art this Saturday at 12:30 The museum is at 318 A Street NE. Call 357-2700.

* The 30-minute documentary "Frederick Douglass: An American Life" screens this Sunday at 1 and 3 at the Clara Barton National Historic Site, 5801 Oxford Road, Glen Echo. An official from the Frederick Douglass Memorial Home will be on hand to lead a discussion after each showing; the program is free. Call 492-6245.