"...what factory load for 243 coyotes..." You'll have to try a box of as many brands and bullet weights as you can to find the ammo your rifle shoots best. The cost of said ammo means nothing.
"...accuracy load for coyotes..." Absolutely. No point in using anything else. Mind you, I haven't used factory ammo for 30 some years.
The rifling twist does though. Mind you, most commercial .243 hunting rifles are rifled for deer sized game. 85's and up. Even the assorted 'varmint' rifles.
The bullet used matters, if you're keeping the hides. Varmint bullets will certainly kill a coyote, but they'll also make big holes in the hide. Don't think anybody is loading hide hunting bullets(commercial fmj's or match bullets) in .243.