Marktheshark: This is a "no brainer" - not even close situation!
Use the 17 HMR!
The several Coyotes I have taken with my 17 HMR have all been one shot kills (Hornady 17 grain V-Max bullets) - I can NOT say anything near the same with the many and varied 22 L.R. munitions I have shot Coyotes with over the last 6 decades.
Go with the 17 HMR and careful shot placement = dead Coyote.
Hold into the wind
VarmintGuy