One sure sign of coyotes in the area...
... is when neighborhood cats and small dogs start disappearing.
I love animals, but I have no problem with anybody shooting coyotes. They are overpopulated in a large part of the US, and they are legal targets on sight, in many states, so long as it is not illegal to shoot in the areas where they are sighted.
In FL or GA, they are fair game, because they are overpopulated and they pose serious threats to livestock and domestic pets.
I know I have at least one friend (a TFL member, for that matter) who has lost a dog (in his yard) to coyotes....