I like 6mm Remington with 58 grain Hornady's for 220 swift performance and better. But the three calibers you mentioned are great prairie dog guns. But you were talking coyotes. The rifle would depend on your style of hunting, I think. If you are calling and shooting close or if you are shooting at 300 yards. If you'll be in the open with wind or in trees, etc.
I know a guy here in SD that shoots a lot of coyotes every winter and in the open. He has kept getting larger more powerful calibers. He says the best rifle for his style of shooting coyotes is a 270 with high ballistic coefficient bullets. If I were to go out glassing for coyotes (I've unloaded all my 270's) I'd likely be taking my 25-06 or 6mm with sleek bullets - ones that didn't blow up easily.
