I guess I stumped everybody.
The correct answer was Glenn. They played an instrumental version of You Belong To The City on Married With Children in the episode called Guys and Dolls. This song is played twice in the episode and it doesn't come on until 10 minutes before the episode ends. When I watch this episode on closed caption, for some reason they have it as the Eagles singing this song.
https://www.youtube.com/watch?v=vYxAoXi6kKc
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This Eagle was the only one to appear on the Common Thread album.