I've never gotten as good of accuracy from the 110's as I have the 125's and130's.
If you think that going to a lighter bullet is going to reduce the damage to the coyote's, you're going in the wrong direction. The lighter bullets will expand faster due to ligher construction and higher velocities. Damage will be even more devastating.
The 125gr Nosler Ballistic Tip has given me excellent performance, likewise the 130gr Speer HP. The last time I was playing with the light bullets in the '06, the 125gr Speer TNT wasn't around. The 125gr Sierra is also outstanding.
For less damage to the Coyote's, I'd recommend using a heavier constructed bullet at a lower velocity. Likewise one of the 150gr FMJ's will ususally produce less damage, unless you hit major bones. In that case, anything '06 is going to do spectacular damage. I tried to take a fox one evening with one of my '06's I was deer hunting with. I shot it through the rib cage mid-torso. Bad idea. Fox was destroyed. Anywhere I'd have shot the fox with a lethal hit would have likewise devastated the critter.
For less damage, I'd recommend the 17HMR rim-fire. Even my .22mag tears up the smaller coyotes at ranges under 50yds. But then, the pelts are worthless in our part of the S.E. USA. Often, they have little or no hair on them from mange mites. I kill every coyote I see as I believe thats how I lost two of my squirrel hunting fiests to parvo-virus. Both had been vacinated, repeatedly but evidently got a variety of the virus they weren't protected against...... Neighbors have lost dogs to parvo likewise. I believe the coyotes to have left the scats with the "hot" virus that infected the dogs. Haven't seen nearly as many 'yotes in the last several years either.......
I've gotten best accuracy with the 125's and 130's with IMR4064 and Win748/BLC2.