I read a lot of complaining about coyotes from deer hunters that think coyotes are killing all their deer. Not so. One big reason that our deer are not in the woods is because they are in farmers fields eating crops and in suburban back yards eating ornamental shrubbery because the browse line is too high in the woods. The browse line is too high because of unnaturally high deer populations for many past years. Hunters wanted lots of deer and they got lots of deer for many years, and now must pay the price. Do you want more deer? Don't shoot coyotes, plant food plots.
Coyotes are primarily rodent eaters. They will also scavenge the rich supply of deer carcasses produced by year round auto collisions and gun and arrow injuries sustained during hunting season. Small thin deer that can't reach the browseline may also be taken by coyotes before or after they die - but these weak and injured deer are going to die anyway, something called compensatory mortality. Deer Biologist Ken Koerth is quoted in North American Whitetail Magazine April 2005 as saying "Coyotes normally can't control deer numbers on their own"
If you want to control coyote numbers the last thing you want to do is hunt or trap coyotes. Billions of dollars, many years of history and biological studies show that coyotes respond to killing by increasing their populations. Killing them causes more females to breed in a territory, breeding females to produce larger litters and more viable pups. Studies also showed that when left alone, coyote numbers declined naturally on their own. It is the people hunting and trapping them that are creating higher coyote numbers. Trying to control coyotes by killing them is like trying to put out a fire with gasoline. Breaking down the social structure of a group of coyotes through the loss of a dominant male or female causes subordinant pairs to breed, where normally they would remain behaviorally sterile. More breeding pairs and breeding by younger members of the group create more and larger litters. Larger litters need larger prey (such as deer) to feed them.
As far as killing fawns, coyotes hunt primarily by movement. Fawns (and nesting turkeys!) stay absolutely still and quiet - this is their natural defense to predation. Any predator must literally stumble on them to get them. However, triplet fawns, ill fawns or those orphaned when the doe is hit by a car or shot with a nuisance permit will be taken because they walk about bleating. These fawns are doomed and is it necessarily bad if they are used by coyotes as food rather than rot on the ground?