I was watching the Game Show Network while Office was installing, and they showed a clip from what must've been a 50's variety show. It was a set of quadruplets (three girls and a boy) doing a version of "Istanbul (not Constantinople)."
I had been under the impression that that song was a TMBG original, but I guess I was wrong. It's funny the things you come across on late night (or early morning, as the case may be) cable.
Update: It was an episode of "I've Got a Secret" from sometime in the spring or early summer of 1960.