For pelt preservation, about the only way with a 7 is with a heavily constructed bullet, heavy for caliber going relatively slow. Lighter frangible bullets will make a terrible mess. My father loaded up some 110 gr spire points in his 300 win mag (not for pelt preservation) going fast, and shot a coyote at about 75 yards.
Have you seen a prairie dog or ground squirrel get hit by a bullet going over 4000 fps? Because that is the only thing I can compare it to. Spectacular, ABSOLUTELY. easy on pelts?? Ha ha. No. After the 10 foot diameter ball of fur floated away slowly in the breeze, all that was left was two bloody pieces of what used to be a coyote.
What I use for coyotes if I want to save pelts is my 22-250 loaded with either a 40 grain or 35 grain V-Max going 4130 or 4190 fps, respectively. As long as you make solid body hits, they do not exit, and make my rifle a 350-400 yard rail gun. However, If you hit the head, or top/bottom of body, it makes a massive splash wound or turns the head inside out. Very violent. My father used to load the 55 grain Ballistic tip in his 6mm remington going right at 4000 fps, but that seemed to be the limit, as that exited on every coyote he shot, with a minimum of a fist sized exit, usually bigger.