Most/all of George Paul's music is square as recorded on the CDs. Most of the later Great Bear recordings are, as well. Otherwise, you have to just listen to a lot of tunes and count them square. Bob Isaacs has a thumb drive full of square tunes, if you reach out to him directly or talk to someone who has taken his workshops.
I've asked many bands for permission to play their stuff for dances where either a band isn't available or the group is new and doesn't have funds to hire a band. All have said yes without hesitation, including those named here. That said, I wouldn't assume that generalizes. You need to get permission to perform music at a dance, or hold a performance license from BMI and ASCAP, which you can buy from CALLERLAB. That's a square-dance group, but the license covers contra (thanks to Bob!).
Alternatively, I've done well hiring bluegrass bands when the state folk fiddlers' convention is going.
--jh--