The .17 in my wishlist in my signature has been on order since August and I had planned on taking a few coyotes with it. Now Christmas approaches and it's still not in so I bought the .223 also listed below.
Like others have said...it's a numbers game - specifically foot pounds! Shot placement is key no matter what, but basically a light bullet like that is going to start slowing down very quickly so in order to hunt ethically with it...you need to be a fair judge of distance or carry a rangefinder...or plot out your site in advance so you know the distances to landmarks.
A CCI 17gr poly-tip v-max will deliver 138 ft-lbs at 100 yards (under test conditions, mind you), whereas their 16 gr TNT Green hollow points deliver just 96 ft-lbs.
Against your typical 'yote I'd say 125 ft-lbs is your absolute rock-bottom for power...so the poly-tip v-max or other catridges with similar performance figures (Winchester 17gr Hornady V-max, CCI 17gr TNT hollow point) at 100 yards should be suitable up to and including that distance...but beyond that you're really pushing the limits of the round's effectiveness.
Even a CCI Velocitor (.22lr) delivers over 125 ft-lbs at 50 yards and under so under those circumstances it is also suitable...but on the bottom end for sure.
I believe there's a 20gr round out there from Hornady I think that would maybe push it's effectiveness out to 125 yds.
Warning!! - lecture to follow.
You shouldn't be bringing a spoon to a knife fight, you should be bringing a .223 or .22-250 instead. I've also heard that the .204 performs very well as a coyote round...although I know no one who owns such a rifle nor have I bothered to look up its characteristics. For a dedicated coyote gun, the factors are very simple:
Initial Cost
Ammunition Cost
Performance
Practical Usefulness
In Ontario you are not permitted to use anything larger than .275 on small game if memory serves, and you are not allowed to use anything greater than .22 during big game seasons if you do not have valid tags to hunt any big game, so that meant that I could toss the ideas of a .270 and a .243 out the window on the basis of practical usefulness...I wouldn't be able to use them whenever I wanted unless I wanted to cough up some money for big game tags. This left me with the .223, .22-250, .204 Ruger, and .17HMR. The .204 Ruger rifle was too expensive for my taste at the time, so that got disqualified at on the initial cost evaluation. The .17HMR just isn't powerful enough to take the animal quickly and reliably at ranges beyond 100-125 yds, which are quite common when hunting these animals on prairie or farmland. So that was out (as a dedicated gun) on the basis of practical usefulness....who wants to hunt coyote with a gun they can only use at 1/3 of the ranges they're likely to encounter? If you're out rabbit hunting with a 17hmr and happen to spot a coyote at a reasonable distance...that's another story.
That leaves you with the .22-250 and .223 and the cost of ammunition settled that debate.