The stupid is strong in this thread.
The situation is simple. Loose pets left outside instead of being kept safe indoors or in a secure yard. There are coyotes in most of the urban areas of the US. They tend to thrive there as people have been and continue to be stupid. You feed them with your trash, food left out and with your pets. If you remove the incentive to stay in the area, they leave. That is not likely to be a viable solution as people will not change their ways willingly or quickly.
In an urban environment you are not going to be able to legally shoot the critters. Should you do so, be prepared to accept the consequences of your acts. Those range from simple misdemeanor prosecution to loss of your rights (felony conviction) to an injury or fatality to an innocent third party from a miss, ricochet or over penetration. Once you launch that shot or arrow you cannot call it back.
You could try poison bait. That might get one or two of them but coyotes ARE smart and there have been lots of attempts to poison them out by ranchers. It didn't work out well. It will also almost certainly be illegal so there is that prosecution thingie again.
Solution. First keep your pets inside at night. That means cats and dogs. Coyotes like to eat both but they absolutely love cats. They will play with dogs run them until they are tired, if foolish enough to chase the coyotes, then kill the dog. If you are going to own a pet, be responsible about it and keep them inside and or secure. If you cannot or will not do that then don't get one.
Call animal control, Call game and fish. Do not take no for an answer. Call the local city council, a LOT. Call the local county / parish representative, a LOT. The more noise you make about it the more likely you are to get a response to take care of the problem. You try to do things on your own expect bad things to happen.
QFT!
Don't get me wrong. I'm 100% in favor of hunting, and coyote hunting in particular. I've trapped them, and I've shot them. It's just not a viable way of protecting the bait you've left out (er, cats). More time, money, and effort is spent every year on killing coyotes, and every year their population and range increase.
Shooting the coyote that's bothering you may be fun, and possibly even profitable (at the right time of year), but it won't be any more effective at stopping the problem than using a spoon to empty the ocean.
If the habitat is suitable, and food is available (and coyotes are some of the most resourceful critters on the globe) you'll have coyotes. Done deal. If you leave your livestock out where they can be eaten by coyotes, you'll have dead livestock. Done deal. Hunting/shooting coyotes even prompts them to reproduce at a higher rate...
We don't have all that many coyotes around compared to Texas, but we shot 41 of them this year here on the farm. Not even a dent in the population...
For that matter, the coyotes are probably better for the environment than the stray cats.
