I "try" not to feed them. I do put out peanuts and fruit for the birds and squirrels during the day and sometimes there will be something leftover. It turns out coyotes will eat peanuts, bananas and grapes!
One of the coyote has mange.
Another has a bad eye and one has a back leg limp. Unfortunately, it is legal to trap coyote in Connecticut. I have one with a mangled front leg that comes every couple of weeks. I am tempted to put out dog food but I worry about the neighbors who have small dogs and some have cats that they let roam at night. So I really don't want to encourage them to frequent the yard. The one with the mangled leg has been coming around since last March so he is doing quite well on his own at least.
I feel especially bad for the little guy with mange. I would like to feed him because I worry that as the mange progresses he will have a hard time keeping warm. Sometimes I don't bother to put the trail cam out because it upsets me to see the wildlife that are not in the best of health and there's nothing I can do to help them.
I had a lengthy discussion with the DEEP here and they said unfortunately coyote are seen as a nuisance and there are no groups to help them. They adopt the attitude of "let nature take its course ". But it's hard to watch.