I have shot the throats out of a few 243 AI's, 12T Hart barrels with zero freebore.
My barrels were 29-30" long, and I used Rem brass, CCI 250 primers, AA2700, and Win 760. The never full length sizing load that shot in the low 2's is 48.5g of Win 760 at 3850 on a 29" 12T, zero freebore chamber. I went up to 50.5g of 760 with the 70g Nosler ballistic tip and got 4030 fps.
Now, with 9" less barrel length than I had, You can do some extrapolation.
A stone cold killer bullet for coyotes if you want max speed is the 60g Sierra hp, tough enough for the largest coyotes, super accurate. The 60g Sierra can stand a little jump.
In my experience, those 55g Nosler bt do not like to jump. If you could ever find any, the 75g Sierra hp is a very jump tolerant bullet.
OP, do you know what kind of throat your chamber will have?
Best of luck to you!