I have two memories of music at the fair in Thomaston, GA in 1959. One was blared through speakers around the midway, and it was THE hit song at the time - "Money", by Barrett Strong. They played hit Rock n Roll songs to "get you in the mood" - to have fun, let loose, etc. Although I am a die hard Beatles fan, I consider this original recording by Strong to be a real classic. It was covered by many many artists, including the Beatles. It still evokes strong, happy feelings of the fair.
The other genre, for which I wish I could find recordings, were those played in the girlie shows, mostly when the girl(s) were stripping. It was a grinding, repetitious sound, mostly saxophones and percussion. I wish I could remember some of the tunes, but they all seemed to sound the same. I was at FSU at the time, and we road tripped to the fair. I can still see the two or three sax players, in suits, doing their little two/three step over and over, and playing the same few bars again and again. It was almost hypnotic. If anyone can provide a resource for this type of music (that is, if my description makes any sense at all) I'd sure be appreciative. At the time, I wasn't listening to the music, it was just there. It was those strippers I was interested in, sho 'nuf. But now, 50 years later, I've forgotten the girls but I can still almost hear the echo of those repeating musical bars. I've often wondered about the life of those musicians.

I'll bet Wayne can help you. He's the expert on all things carny!

He may pop in here or you can email him through his site:

http://goodmagic.com/carny/index.htm

Sorry, this is a "musician skill", I'm sure, probably easy for a musician but I'm musically clueless,

The tune Night Train was used by a lot of strippers. It has a nice simple, but catchy rhythmic melody. https://youtu.be/pcs7FAH63Fg

My Baby Does the Hanky Panky

Thanks for that link Jerry. It's a wealth of knowledge