I hunt them for both sport and predator control. When raising a litter, coyotes become a little more likely to try to make an easy meal off of livestock. So I don't let off of them. I just shift my hunting from open areas to closer to herds that will be calving. Seldom will a cow ever calve that a coyote isn't watching somewhere nearby for any sign of weakness.

Many of the coyote pups will not survive their first couple of months due to starvation. Even shooting the parents won't have much of an impact. That just frees up food to boost the survival rates of the others. So if you feel like hunting them, go for it. You will have no noticeable impact on the population.