best advice, is fence in your yard so they cannot get to your small dog!
odds are its illegal to hunt in the city limits, so your not going to find anyone to do so, and odds them getting ALL them,. is slim to none! they will keep coming back as they reproduce!
so the better way to protect your small dog, is make your property coyote proof, and not try and kill the coyote's! is a never ending game you will never win!
wish to be a pet opener, it comes at a costs to you, to protect them!