either the 17 or 20 grain will work just fine. I typically shoot the hornady 17 HMR® 17 gr V-MAX or the hornady 20 gr HP XTP. The 17 grain v-max has a polymer tip while the 20 gr hp xtp has a hollow point tip.
Both the 20 and the 17 have the same knock down power at 100 yards (137) and 200 yards (72). The only difference is the muzzle velocity. The 17 has a 200 fps greater advantage than the 20 grain at 100 yards. The 17grain also shoots flatter out to 200 yards, but not by much.
Just make sure you keep your distances in. Sure, you can hit them at 200 yards, but the power just might not be there. Keep them inside 150 and make sure you have an accurate shot. Test both rounds in your gun first. My savage 93r17 didnt group the 20 grain like it did the 17 grain. So I went with the 17 grain. Test and test again.

THE BEST IS 20GR 17HMR ROUNDS. But 17-20gr is okay, nothing smaller. Even with a 20gr you want a close range shot of less then 100yds. 50yds would be ideal. If you put a poor shot on it with a 17hmr, it will run and die a slow painful death. But a well aimed shot between 50-100yards with a 17gr or 20gr bullet and it will die almost instantly. Check local laws first though.

Unfortunately I do not have experience with Coyote hunting. I'd recommend maybe giving Hornady a call to see what specific 17HMR round they'd recommend.