Been there, debated that...
17hmr 22mag coyotes under 100 yds
22 vs 17 hmr
Frankly, either are going to work. To call one "ideal" over the other is mostly subjective. Some guys say "use the .17HMR for longer shooters", other guys say "use the .22WMR if your game is over 30lbs". If we're 100% honest, a skilled shooter with a good rifle and the proper bullet choice can reliably take coyotes to 100yrds with either of them, some guys even farther.
Personally, I have both. Both work, honestly can't say I see much real difference on coyotes to 150yrds. I've had success with both, and admittedly I've had failures with both. Sometimes dogs just don't want to go down fast enough to find them.