I talked to a biologist about having an effect on coyotes, and he told me that, I would have to hunt coyotes harder than I hunt deer, to make an impact on their population. He also said the biggest problem for predation of young deer and fawns is local dogs.
He went on to explain that coyotes kill to survive, and will consume the entire kill. Where local dogs kill for sport and fun, they may eat some of the kill but mostly play with it, and then go try to find something else they can chase, because they are getting fed by their owners.
I wish AL would put a bounty on them like some counties in the State of Texas. http://texassportsmansassociation.org/coyote.htm
The main reason they have these types of bounties is because of the goat and sheep farming, but I have hunted places in Texas where coyotes or bobcats were not to be found, because of the bounty.