I've added the 22 hornet and 218 bee back into the mix.
Well then, why not add the improved versions of these two as well (17 Ackley Hornet and 17 Ackley Bee)?
Ladobe, you speak very highly of the 204 as well as the 17's for coyotes. As I get the message from you, they do a fair to excellent job taking coyotes. I have only seen one coyote killed with the .204, and it certainly did a very fine job. With fur prices down and deer and antelope also down, we have been after coyotes more as predators than fur bearers. I was interested in your comments on these calibers as you obviously have experience with them. Here in Wy. the 17's are not too popular, mainly due to wind I beleive. The 204 has a following, but not in my circle of shooters. It is interesting to see what others consider good calibers for their hunts. I have thought of a .204 several times, but the couple guys that have 'em mainly shoot p. dogs with them.
Don't own a 204 myself, but friends do and I've seen what they'll do. IMO the 17 Rem (and the wildcats that match its ballistics) is just about the perfect coyote rig... "for fur". The 17M4 is a close second.
Spent lots of time in western WY/MT in my life (hunting, fishing, canoe river running and working), so know your conditions pretty well. My family had vacation cabin's near Wilson, and at Mack's Inn in Island Park, so not hard to figure out where I spent lots of my summers growning up and vacations after. As a teen I worked 3 summers in YNP and over the hump in Victor/Driggs as well.
If you don't care about the fur and want to keep it simple, just use your big game rigs. In a pinch I shot a lot of predators with the 270 Win I hunted mule deer, elk and pronhorns with for a few years. A 243 Win would be a great coyote choice. If you want even less recoil try a 22-250. Both will buck those winds there well enough to cleanly take coyotes as far as you'll normally shoot them.
A few years ago the ranches I was doing ADC for was getting a lot of pressure from their ranch hands taking pot shots all week at the predators. So they were hanging up long, sometimes very long. Coupled with the high winds common there sometimes, they really were pretty much getting to be a free pass thing with the regular dual purpose predator and varmint rigs I usually carried. All my 6 and 6.5 wildcat's were heavy rigs, so I bought a new Winchester Featherweight Deluxe in 243WSSM just for those ranches because it would be light to hike with, they buck wind well and shoot very flat. Never got around to using it because of health issues, but it sure would be a super coyote rig if you don't care about fur.