I took a big doe 4 yrs back with a taurus 357 6in. She was 42 yds out and dropped like a sack of potatoes with 158gn XTPs. Took both lungs and heart on that one. This is the smallest caliber handgun allowed in Ohio, and rifle is illegal. That only leaves shotgun, handgun, and pointy sticks. (and the muzzle loader).
If you can't shoot quality, try quantity.