I've used lots of calibers to shoot 100's of coyotes over the years. My favorites were the 220 swift and 22-250. Very Very few have gotten away, most of the ones that did............would have even with a bigger caliber(poor shot placement, leg hits). I've taken a fair number of song dogs at 400 to 500 yds with the fast 22's, no problem at all with decent shot placement. I have had a couple get away that were beyond 500 yds, and they were shot with a 6mm and heavy bullets designed for deer size game. Don't know where they were hit, could just tell that they were.
I've shot the barrel out of my old Swift(made in '73) and am currently getting it re done in an Ackley Improved 6X47 Lapua. My other choice was a 22-250 Ackley, but the smith I'm using prefers to work with 6mm's; so I thought I'd give the 6X47 Lapua case a try. Still have and use a highly accurate 22-250 that shoots Bergers great.....knocks coyotes DRT usually and doesn't tear up much fur.