The Birdwell House Band (also abbreviated as Birdwell Band) plays town music in season 3.
You actually see them play in Muddy Buds Hit the Suds and they also help give Clifford a bath there.
Even though there are 4 members (2 males 2 females) only two of them are mentioned in the end credits of BOTH stories of the episode, including Lights, Camera, Clifford