The 17HMR isn't really a coyote round, but it can work at SHORT ranges. 50yrds or less. Hitting a groundhog at 165yrds doesn't matter for coyotes. A wrench can be used to drive a nail in a pinch.

The 223rem with a fragile built bullet like the Hornady V-max or Winchester Ballistic Silvertip in 50 or 55grn is a much better option.

You're wrong here. A 17HMR is just as apt to ricochet as any other cartridge, and to be honest, MORESO likely to ricochet than many other rounds. If you're worried about accidentally clipping one off into the side of somebody's house a mere 50yrds away, you shouldn't be shooting there, whether it's a 17HMR or a 223rem. Is this a spot that you bowhunt? Give that a whirl, it's a real rush.

A 30lb coyote isn't a 6lb groundhog. You don't have the luxury of a 6" vital circle on a coyote with a 17HMR, nor really with a 223rem.

Headshots are the better option with the 17 and only to the 50-75yrd mark. If you can field shoot a golfball at 100yrds, then 100yrds. Vitals shots are marginal at best with the 17HMR at longer ranges - and by longer, I'm talking 100yrds. You won't be worried about recovering "every one" if you're taking such long shots at coyotes with a "hummer," you'll need to be more worried about recovering a "single one," as my experience has been that even well hit with a 17HMR, they coyotes are going to run.

Green is fine. How you use the light matters a lot more than light color.

End of the day, the 223rem will be a better option for you, all the way around.