What load do you use for 243 on coyotes? I have been using 87grain hornady v-max they work great they just makes a big hole.

In a .243 I like the Hornady Outfitter ammo which is a 80 grain cx bullet. Solid copper with a tip. Less damage usually. This is slower than your bullet. I use this for hunting everything. Try it.

The V, stands for Varmint, Max is for maximum speed, wrong bullet choice for your purpose. Too fast and expands to much for that small of a thin skinned target when you are saving pelts. Big holes.

I prefer the bullets designed for medium game over varmint bullets in my 243 if pelt damage is a concern as stated above.

The 87 gr. V-Max is what my son uses on antelope with great results. In my 243 for coyotes I have always run the 75 gr V-Max or a 70gr. Nosler Ballistic Never had a coyote argue with either but both are not fur freindly. Most of my rifle work on coyotes is for damage control so fur preservation was never on the table. My dad ran FMJ bullets in a 243 for fox and coyote. These do much less damage. Try not to hit a shoulder with anything if you want the fur.

I’ve literally shot thousands of P243H rounds from federal. I’m not sure how many coyotes that translates to over the decades but it’s a big bunch.
It’s a 55gr Nosler ballistic tip. I’ve no complaints.

Osky
Edited to add I’ve taken elk, mule deer, whitetail deer, antelope, bears, wild pigs, wolves, javelina, cougar, and I’m sure a few other critters I can’t recall at the moment.

I just use my deer rounds and that hornady North American whitetail the last several years in both 243 and 7mm-08. Coyotes die just fine and they don't blow up and make as larg of homes ad varm bullets unless you hit a lot of bone. When I hit boat the bone turns into shrapnel and makes large holes.