All good stuff said so far. 223, 22-250, 243. It's all just whatever caliber you decide you'd like to use, all would do excellent for coyotes. If I had to shoot just one caliber for varmints though I'd make it a 22-250 as it's one accurate, flat shooting caliber. A 223 would be the cheapest to shoot and a 243 really knocks them flat out pretty far. A 243 would double for a nice deer gun as well if it's legal in your area. If you just want something that is accurate and ammo is cheap go with the 223. It will kill them just as dead as the others with good placement out to 300 yards. If memory serves me right, a box of 40 45gr Winchester hp's at Walmart is $11.98 and a box of 40 45gr Winchster hp's for the 22-250 is $16.98. Yah, so I probably confused you more, but what I'm saying is either of the 3 would be an excellent choice and you wouldn't go wrong with either of them. Good luck. Regards,
Matt