For coyotes: either a .22-250 or a .270. It's really irrelevant which caliber is used. Most calibers will do the job if the rifle is sighted in properly, has fair-good accuracy, and is in the hands of a shooter who is familiar with where the bullet will land at any given distance and in any wind condition.
My .22-250 single is bench-rest quality, weighing in about 13 pounds with scope; the .270 Mountain Rifle is far lighter. I use either one, depending on how far I have to walk to get to the set. I don't collect pelts, so I am not concerned with how much damage is done to the animal.
Using the single-shot forces me to be more critical of my making good shots. I have one chance. If I miss, the dog usually splits and I have only myself to blame for not making the shot. An AR in .308 or 7mm-08 would be nice, but I'm used to the .22-250 and am familiar with the bullet trajectory. I usually don't miss, but then again, I have to pick my shots. I use a FoxPro
CS-24 caller, plus hand calls and try for maximum concealment, minimum movement, scent-control, and all that good stuff.