There’s no magic bullet weight for certain twists, you’re just limited to a certain length bullet with a given twist. Many factory 243 rifles are still made with 1:10 twists, my Tikka T3 lite is one. I’ve only used up to 95 grain bullets in it, but I’d not be afraid to try 100 grain SP hunting bullets either. I’d expect 105s wouldn’t stabilize.
So, a 10” twist 243 should shoot bullets from 55gr all the way up to at least some 100 grainers. Obviously your local atmospherics can play a role when dealing with marginally stable bullets.
For which to use on coyotes, I shoot them with whatever I have on hand, just to eliminate them, usually 95 grain bullets. But I think if I was loading for dog hunting specifically I’d try 75 or 87 Vmax, or 70 Nosler BT. 55gr Vmax or BTs would shoot really flat and I’m sure would wreck coyotes.
For all around killing bullets I like 90 and 95 Nosler BTs, but I shoot pigs more than coyotes.