Not sure what your end goal is, but I just put a .223 on my .45-70 BC Frame and it's a very accurate heavy barrel in 1:9 twist. The nice thing about the .223 is lots of ammo deals around for it. Was there a particular reason you wanted .222? Just curiousity on my part. 
The 222 is the Parent cartridge to the 223. Generally, but not always, it is more accurate than a 223. The 222 held many benchrest records until the 6 PPC came along. If I am not mistaken, it still holds the world record for the smallest 5 shot group at 100 yards. Further the 222 is a 1-14" twist cartridge and the 223 was a 1 - 12" or 1 - 9" cartridge. The 223 getting the faster twist as a bow to it's military heritage where heavier bullets were employed. It's military background gave rise to it's popularity, cheap brass and cheap or free ammo - not because it a better cartridge. The 222 was designed for 52 or 53 grain bullets; thus the 1 - 14" twist that was used. As easy as the 223 is on barrels, the 222 is even better. There is about 150 fps difference in the two with the nod going to the 223 of course - 3150 vs 3300 for a 50 grain bullet or there about. Not really that much for a higher pressure round. Believe me, if you use a Hornady 50 grain SX spire point, it really does a number on a woodchuck in a 222. That bullet was designed for the 222 Remington to give explosive hits on critters like the 220 Swift had done for years. Then there is the nostalgia thing, like a 22 Hornet, or 45-70 for instance. There really is really no good reason for them to exist. There are other cartridges that can do the same thing as cheaply and as accurately, yet manufactures still make rifles and people still buy them. They still make a few 222 guns besides the H&R there is the new Savage Model 25 and CZ that spring to mind and you can get custom barrels from most any one who manufactures barrels - some with custom neck sizes.
After saying all of that, I presently do not own a 222 Remington and presently have 2 - 223's. A 223 is a bunch easier to get than a 222, because of the cheapness (military background) of the ammo, not because it is a better cartridge. I still have the RCBS precision dies (old style windowed seater) and brass for the 222.
I have been very tempted to get a 222 barrel fitted to one of my frames,
but the 1-9" twist rate has me thinking I want to go in a different direction. 1 of my 223's is 1 - 12" twist (H&R) and the other is 1 - 14" twist (Shilen) and have a spare 1 - 14" A&B for a Savage. I am not a fan of heavier bullets in a .224 caliber unless I can push them at 3000 fps or faster for the really long shots. I presently have a 22 BR with a 1 - 8" twist with 75 - 80 grain bullets in mind. The 2 - 223's with 1 - 9" twist had both of their barrels pulled for a slower twist rate.
Good Luck and Good Shooting
