I've done a sheep skin and a section of buffalo hide. The key to having the skin come out nice and flexible is to work it over a something like a smooth wooden beam. You can also work the hide back and for by hand. The purpose is to break up the fibers in the skin. Otherwise, the skin will tend to stiffen up, even though it's tanned. This probably won't be much of an issue on coyote type skins, but sheep and buffalo skins are a little thicker.
You can also just stretch and dry the pelt as if you were preparing it for sale to a fur buyer. I've got a couple on the wall that are just dried and they look fine.