I hate coyotes so I would say kill as many as you can whenever, however you can. They are the #1 killer of fawns. An article in American Hunter claimed that coyotes are responsible for 87% of fawn fatalities.

It would be tough for a coyote to take a healthy adult deer. Most of their diet is actually bugs and small rodents. However, this time of year they will try their best to dine on fawns.