Back in the late 60s and early 70s I killed several dozen with a
22-250 while they were eating our peanuts and soybeans...Never had a problem killing them with center lung shots or lower neck shots...I was using Remington 55gr bullets...I bought a .243 in 1980 and now use it for everything from crows to black bears...
About 10 years ago one of my brothers traded for a 22-250 Remington 700...I sighted her in with Federal Premium 60gr Nosler Partitions...This is my nieces deer rifle, at last count she had killed 14 deer with this gun...Never lost a one and most dropped in their tracks to high shoulder shots with a good exit, I know because I have helped her clean 6-7 of these deer...
It is perfectly legal in North Carolina to use a .22 for deer, the Regulations simply don't adress this matter...I guess we believe in less Government down here...
Some of us started hunting when we actually went for food, not antlers...We used whatever gun happened to be avaliable...We didn't have "deer" rifles or "varmit" rifles, heck I've killed several deer with a .22 rimfire to the brain while squirrel hunting...
Stick with the 60 grainers that are made for deer and you'll be fine...