If you are looking for the band that composed the hit song '74-'75 see The Connells
The Cornells were a 1960s Los Angeles band that played mostly surf music. Four of the five members had a parent that was a well known celebrity.
The band appeared on the show I've Got A Secret in 1963 with the secret "We're all the sons of Hollywood Celebrities. They played Caravan live on the show.