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.
Hunting is not usually a pursuit where instant gratification abounds. It takes a lot of time, practice, resources and patience to be a successful hunter. So when someone decides that an area they hunted only once without taking an animal is worthless and devoid of game, I don't quite understand it. These people usually jump from game management unit to game management unit; trying a new one every year.
Now don't get me wrong, there are people that just enjoy scouting and hunting...