Coons are nest predators and they are the primary cause of the demise of the Bob White in the South. I'm sure they will work on turkey eggs, given the opportunity. Coyotes are opportunist predators that primarily hunt live prey. Both need to go. Be careful with hawks as they are federally protected. The Possum Police frown on trappin' 'em.
Two experience with coyotes.
One in NW FL on Eglin Reservation. Workin' a stubborn tom and next thing I know, I see a blur to my right, comin' thru the air. Had to knock off his charge with butt of my scattergun.
Was knocked off balance and couldn't get a shot.
The other was on private ground in KS. Had a lone hen deke out and he walked by it til' the wind made it move and he jumped it. Left in lyin' once he discovered it was a fake. Didn't shoot for fear of spookin' the gobbler I was workin'.
"Chasin' gobblers has a lot in common with dealing with a wife, 'bout the time ya' think ya' got 'em figured out, they change the rules!!!"