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.
If you're lucky enough to be on private land and can leave your stand up during the off season you can tie an old piece of cloth or something of the sort to your stand. I like to use an old camo bandana that I have. That way the deer get used to the movement and eventually don't bother even looking up when there is slight movement. This may just give you the time to draw your bow or raise your gun without being detected.