Pretty much anything you shoot out of a .308 is going to kill a coyote. If you have a basic deer load that shoots accurately in your rifle, just use that. Or just buy some inexpensive 150 grain soft-points and have at it!
A while back I was going to do the same just to do it. I had settled on the 110gr Varmagedon's. In the end, I didn't do it because I didn't feel like switching scopes again.
I've used 110 v-max, 110 varmagedon, and some 168gr gold medal match like someone said above, almost anything out of that rifle is going to destroy them. A spicy 110gr varmint bullet makes a real mess. You can shoot them bad and it will still nearly cut them in half.
Don't Handload . use TAP Hornady 110 vmax, it was a good factory 308 Varm. load .. also, Federal has factory 110 vmax .308 ammo .
to mimic the TAP 110 factory with Handload use 110-Vmax's . . 43.7 Reloader 10X .. it's a comfortable 3150 Vel. . 22" 5r out my rifle.
you dont want to handload but, 125 grn. Speer TNT's work real well also .
Light bullets work great. They will start dropping off good on your downrange holdovers after 300 yrd. but still friggin accurate and energy for dropping them on the spot.
.
What he said. What does your rifle like? Mine shoots best with 168gr CoreLokts, so that’s what I feed them. I’m not worried about fur, I just want them to die.
The only other consideration would be a lower chance of ricochet with the light varmint bullets in that caliber vs something in the 150-168 class. FWIW I don't think I've ever had the 110 Vmax NOT shoot well in anything I tried it in. Very easy bullet to load.