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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 show, were aged up into teens and given their own program on [http://www.imdb.com/title/tt0066699/ 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.