Ideally, if you plan on saving fur, you want a bullet that completely expends it's energy inside the animal without exiting. My first choice for winter time coyotes and foxes is a .17 Remington shooting 25gr Hornady H.P.'s.
I've shot a bunch of coyotes with a .22-250 and 40gr VMax's, which works great with a dead center hit, but makes and awful mess if you fringe one. If you're shooting a larger caliber (.24/6mm, .25, .270, etc.) and you want to save the hides, I think it's best to avoid the polymer tipped bullets and hollowpoints all together. With the larger calibers, I'd suggest you use the same bullet you use on big game. Sure the bullet will likely pass completle through the animal, but the theory is that you'll have a small entrance and a small exit hole.
Good luck.
