That bit of basketball history belongs to Keith Rice, who began playing at BYU in 1977. Danny Frazier joined the team in 1978. However, I am not going to say definitively Keith Rice is the first African-American to play for BYU, but he is the first that I know of. From the Deseret News 6/15/2018 "Guest commentary: Incoming transfers to BYU basketball have historically made major impacts" was this quote "One of the first black players at BYU was Keith Rice, who came to BYU from Mount Hood Community College in Oregon, early in the tenure of head coach Frank Arnold. Rice helped lay the foundation for a resurgence in Cougar success during the Danny Ainge/Fred Roberts/Devin Durrant era."
https://www.deseret.com/2018/6/15/20646779/guest-commentary-incoming-transfers-to-byu-basketball-have-historically-made-major-impacts.