Great question.  Typically a felon is not allowed to own a firearm.  BB (black powder guns), certain length knives, etc. cannot be owned by felons because of their intended and unintended uses.

If you feel you may qualify for a sealing of your record and or expungement of your record (you do either to restore your rights so you may be able to carry such weapons), then consult with a criminal defense attorney in Georgia to see if you qualify for these proceedings and have him or her help you with the process.

Try www.attorneypages.com to locate such an attorney.  You can then check his or her record at the Georgia State Bar.