Can I own a gun if my wife is a felon?

Just because you have a felony record does not preclude your wife from owning a firearm. As a felon, you could not own or possess such a weapon. If you live together, and your wife wanted to have the weapon in your home, it would require her to keep the weapon out of your possession and control.

What kind of self defense weapons can a felon own?

Alternative Protection Protecting their home can be accomplished with other means than a firearm. There are certain weapons that felons can possess that are not considered to be firearms. These include a knife with a blade not longer than four inches, a muzzleloader, a crossbow, and a pellet gun.