The Bedrock Rockers
Hanna-Barbera cartoon characters Pebbles Flintstone (voiced by Sally Struthers) and Bamm-Bamm Rubble (voiced by Jay North), mere infants in the original animated tv series The Flintstones, were aged up into teens and given their own program on The Pebbles and Bamm-Bamm Show. They were also given this Archies-sounding pop band with their friends, Moonrock Crater (voiced by Lennie Weinrib), Penny Pillar (voiced by Mitzi McCall), and Wiggy Rockstone (voiced by Gay Hartweg). I think the band may have also appeared on The Flintstones Comedy Hour.
Two of the songs performed on the show were "Yabba-Dabba Doozie" and "Sunshine Man".
If you know your Flintstones, you'll recall that Pebbles and Bamm-Bamm become famous as infant musicians in the "No Biz Like Show Biz" episode (09/17/65) of the original series. Then you'll also recall it was all a dream Fred had.
See also Mick Jadestone and the Rolling Boulders.