If your state allows .22 cf's it'll likely be a handloading situation for proper bullets to handle deer,,,jmo.
Otherwise the .243 will do you just fine with light recoil. The mention .260 and 7-08 are good ones also. Or there's the option of specialty pistols such as the TC's . With practice they will hold there own with some rifles.
In case the later interest you,, http://www.biggamehunt.net/node/25095
243, 260, 7mm-08 all good rounds for deer and will kill out 300 yards if you do your part. If your shouder is real bad, you should stick with the 243 or 260. I perfer the 260 because it has good bullet weight (120gr-140gr), high section densty and high BC.
Hey, look into the 6.8 SPC cartridge. I have one in a Stag ARMS AR-15 and it performs wonderfully out to 300 yards and it has less recoil than the .243 Win. It shoots a 270 cal bullet and I shoot a 110 grain Sierra Pro Hunter bullet from Silver State Armory. I believe remington and ruger and T/C chamber it along with many of the "black guns" like Stag arms and DPMS. I used this cartridge on a large doe in MN this fall at over 300 yards and she was toast after a thru and thru front shoulder shot. Great knockdown and very little meat damage. Look into it, It is a fun, short, light recoil caliber.
Here is a tip that was passed along to me - and I have not tried it yet - but it looks (and smells) like it will work fine! The gentleman that gave it to me regards it as his secret weapon and he is a VERY successful hunter.
Get a fresh tarsal gland off of a decent buck - I think the ranker, the better. Taking them off of bucks that are hot in the rut seem to be the best because that is when the glands are the darkest and have the most "male buck" scent...
Take that gland and put it in a good,...