I tried 30 carbine 110gr bullets in my marlin 30-30 and didn't push them as hard as you are. They never did shoot very well. I have owned 5 marlin 336s and a glenfield model 30 with a half magazine and everyone gave good groups with 150 and 170 gr bullets. I really like 30-30s and could do all my deer hunting with one and never need more gun. Its a great handloader cartridge.
If you want to shoot coyotes at 200 yards you might want to get your daughter a 223-243 type of rifle. Since you handload a 243 with 80gr loads reduced to 2700-2800fps should be a light kicking round and be fast enough for 200 yard shooting. Plus 100gr bullets could be her deer rifle. Maybe a light rifle like a savage youth or a ruger american rifle.
I haven't handled the savage but did get to look at the ruger. It seemed like a fine rifle for the low asking price. Too bad they don't offer it in 223 or 22-250.