I live on a ranch in Texas and we have coyote problems - a single coyote isn't a problem but a group of them can be, especially with your dog. I would not worry about kids, fish, etc. but I have seem them pack up on domestic dogs and kill or injure them. They have taken out 3 or 4 of my Texas Dall grown sheep and of course will kill deer when given a chance. Again, the only concern I would have in your case is your dog. Best method other than gun is a snare. If you can find where they are entering your property (assuming it is fenced) then a simple snare attached to the fence will trap some of them. They tend to dig under fences and cross at the same place on regular basis - often times you will find some of their hair on a barb wire fence where they are crossing.