Noise CAN e a problem. Talk to your nieghbors. Discuss the coyote problem with them and tell them your plans (with the PD's blessings) and IF you do try and let them know which nights (if possible) you will be setting up. IF they are also having Yote problems they will probably be receptive to your approach, working with the police and INFORMING they of your intentions.

Weapons to use? IF you have a good area that will take care of any missed shots or ricochets go ahead and use a varmint round (the 17 would seem to be good for this) but be extra careful to take your shots with the thought that ANY shot could do astray and shoot accordingly.

I know this sounds really PC, but sometimes there is no choice.

Hope this helps you with Your Yote problem and gets the Neighbors on YOUR side.

PRESENT IT TO THEM AS A PUBLIC SERVICE!