Wes is right on in his above. For years in Maine I killed about 75-85 coyotes per year during my time hunting and also guiding. Most were big and primed out. Most were >35lbs but probably 1/3rd of the yotes that me or my sports killed were >45lbs depending on what time of year we hunted.
During calling or over most bait locations I used a 223Rem/24"/1:9/AR. I shot hundreds using a Sierra 52gr BTHP. Eventually I switched to a 40gr NosBalTip.
I found that if I hit bone going in there was never an exit. Even if it was just a rib,however I always tried to put it square on the shoulder.
My vote is for small and just as fast as you can move the bullet. I am not familiar with some of the newer thin jacketed "varmint" bullets of today so I cannot give first hand knowledge/info on those.
For the intended purpose I would also add . . . use the fastest twist bbl that you can. It will help to pull the bullet apart on impact.
Good Huntin' --- SAWMAN