A Savage in 204 sounds like just the ticket. I got to use a 204 and a 22-250 P-Dog hunting, and I was more impressed with the 204. Damage seemed the same, except I didn't have to hold off for wind as much with the 204, and recoil was much less, I could see hits every time.
Here's the perfect coyote gun-
Predator Hunter

[ul][*]Chambered in .223, 22-250, and .204[*]Internal box magazine[*]22" medium contour camo barrel[*]Synthetic camo stock w/ rounded forend w/ 2 studs[*]Oversized camo bolt handle[*]Weaver style bases[*]AccuTrigger adjustable from 1 1/2 - 6 lb[*]MSRP $691 [/ul]
I saw one for $500 in SD when I was at Nationals.