A 17 or 20 grain bullet is too light in my opinion. The reason is that with higher velocities, more weight is required to maintain stability, regardless of calibre, so I am not picking on the little .17 for any particular reason.
It was just a bad mistake from the start
I've not hunted coyotes with a 17hmr. However I think the 17gr ballistic tips are too frangile. If I used an 17hmr, I would go with either the 20gr CCI FMJ or the Hornady 20grain HP XTP bullet. A bit heavier and harder.
Dad shot one full of puppies 3 times last weekend all in the vitals....but she kept going like the energizer bunny....LOL...then....my .300 Winnie Mg screamed alive and cut her in two...didnt even wanna bother with pics....nothing left to take pics of...lol
Not too small if you don't want to find them. They're going to run a ways almost every time. Coyotes are tough. I tried mine on one and hit him square in the chest and I never found him. I'm sure he eventually died but that doesn't do me any good. My farts weigh more than 17 grains. You can't expect that small of a bullet to drop a coyote.
I have seen my dad shoot two coyotes with the .17 HMR shooting 17 grain ballistic tips. One jumped straight up about 4 feet and hit the ground dead, the other hit the ground like a sack of potatoes. Neither shot was past 60 or so yards, though, and both were 'boiler room' shots.
I hit a bobcat at eighty yards right square in the chest frontal shot with the 20grain FMJ's and it leapt straight up into the air about three or four feet turned and was gone like lightning. I looked for a blood trail and zigzagged that ground for a good while and didn't find anything. I love my 17 and would shoot at a yote out to a hundred if I had a good head or boiler room shot while bunny hunting, but if I am specifically hunting yotes I am grabbing my 243 for anchoring ability.
Try to put your tree stand in a tree with plenty of background cover, keep the prevailing winds for that time of the year to your face, and take care of those pesky squeaks and creaks your stand may have developed while sitting in the shed. A good treestand lube can be made by heating petroleum jelly until it reaches a liquid form. Some hunters have reported success by including a cover scent in this mixture before applying it to their stands.