RE: coyotes
As has been stated I believe by Rob,coyotes are opportunistic killers.They will kill deer mature or otherwise if given the chance.I have witnessed a mature doe being killed in deep snow by two coyotes.I didn't have a rifle with me unfortunately.
Likely the only way to seriously effect their population is to trap aggressively,otherwise the females will just self regulate their litters to make up for their declining numbers.