Let everyone be armed. Then it wont matter if you have a criminal record. Only an idiot would use a gun in such a society when the chance is very high that a criminal would not live that long if he/she were intent on harming someone.
I honestly believe that everyone, including convicted felons should not be prohibited from owning or carrying weapons. But I also believe that punishments for crimes involving a weapon from brandishing to robbery to murder should be very harshly punished.