I am not a coyote expert by any means.The area in which I live has a plentiful coyote population.I know that than when the coyote population is prolific we see a reduction in the amount of fawns.Our bear population has also risen quite significantly in the last several years and they put a hurt on fawns as well.
I have witnessed 2 coyotes kill a healthy adult doe,and I have friends who have watched coyote's work a deer in to an area where the deer was necked down in to an area where the alpha dog was waiting.Lastly while turkey hunting I have had coyote's come in to me from different directions they were coming to my calling.
As it relates to my killing them,if it is in season and I have the opportunity they get shot.I have never specifically hunted them but I have shot several.