Yea, I hear you on the coyotes. There's been a ton of people trying to get into coyote hunting
in the last 10 years. 20 years ago, only us dye-hards were out chasing coyotes and a guy could hunt just about anywhere. Ranchers would even give ya references if they saw you were good at it.
I am suprised to hear that people are charging a fee to hunt coyotes however. I don't allow any on my property for the simple fact that I am selfish and hunt/call them myself here year round (if I can find time off work).
I think there are quite a few landowners that will allow prarie dog shooting without charging a fee though (I know there is here, not sure about by Gillette). Maybe check with the chamber of commerce or the WY game and fish. I bet there is a local warden or biologist in Gillette somewhere.
Best o Luck, Happy New Year.