I've got "coyote" guns spanning from .17 Rem, .204, .223, 22/250 and 22/243 Middlested. If you can get a easy handling 22/250 sporter that shoots like a heavy barrel, you can close the book on coyote calling rifles.
My current favorite is my Kimber Varmint, Leupold 4.5-14 X 40 LR with Boone & Crockett reticle, various Harris bipods, sticks or a military sling depending on set up or mood. It weighs 8 1/2 pounds ready to go, just like most of my hunting rifles. I've found that 12 pound rodent rifles that might be great for a 400 yard shot are a real handicap the rest of the time. Doesn't stop me from using them at times, but very little about coyote hunting makes sense.