In some areas, it might be possible for coyotes to kill 40 deer. Notice I said coyotes, not a coyote. Generally, it will take several to kill a deer, therefore the 40 deer/1 coyote becomes 40 deer/10 coyotes or 40 deer/80 coyotes. As stated above, if a predator overhunts its prey, the predator will soon become scarce.
It's also based on a misconception that coyote eat deer exclusively. In studies I've read, over 90% of a coyote's diet is composed of rodents and small animals (rabbits, moles, skunks, shrews, lizards, snakes, etc). About 5% is vegetable matter (berries, fruit, sweet grasses, etc). That leaves about 5% for stuff like deer, cattle, stray cats, Pomeranians . . . Oh, sorry!!