A.S.
Not sure about this one but I'll go for it.
I used to hunt with my dad before I got married. We spent a considerable amount of time hunting deer, dove, turkey, and quail. When I was growing up it was always for food. If we didn't get a deer over the winter we would be in danger of not eating meat a significant amount of the year. I have since not participated in any hunting trips because of kids/work/other obligations. My husband does not hunt at all. Although we did it for food for the most part my dad continues to hunt for fun and relaxation. I loved sitting out in the quiet and just being with him. I have never hunted something like coyotes but I can see where the population can become a problem.
I don't know that it is right just to hunt them for fun. I think "to control the population" is missing something if it's just for fun. Do you have to have a license to hunt a coyote or is this a recommendation from your local Parks and Recreations Department? If you are seeing more and more it may not necessarily be an overpopulation - it may mean they are just moving into the area. Have you considered contacting someone to see if they can relocate the population. While they aren't considered endangered just hunting them down because you think it's necessary is how some animals ended up on that endangered species list. I'd like to see a recommendation from a reputable source before making a decision like that.