The easy answer? The only way for a convicted felon to own a gun in Oklahoma is to have their civil rights restored through a Governor's Pardon;

The Governor of Oklahoma, through the constitutionally-granted pardon power, is the only person who can legally reinstate a convicted felon's right to own a firearm, work in law enforcement, and be a gunsmith.

The Governor's ability to pardon convicted felons is found in Section 10 of the Oklahoma Constitution:

The Governor shall have the power to grant, after conviction and after favorable recommendation by a majority vote of the Pardon and Parole Board, commutations, pardons and paroles for all offenses, except cases of impeachment, upon such conditions and with such restrictions and limitations as the Governor may deem proper, subject to such regulations as may be prescribed by law.

Without a Governor's Pardon, convicted felons are prohibited from possessing firearms by 21 O.S. §1283, which states that:

A. Except as provided in subsection B of this section, it shall be unlawful for any person convicted of any felony in any court of this state or of another state or of the United States to have in his or her possession or under his or her immediate control, or in any vehicle which the person is operating, or in which the person is riding as a passenger, or at the residence where the convicted person resides, any pistol, imitation or homemade pistol, altered air or toy pistol, machine gun, sawed-off shotgun or rifle, or any other dangerous or deadly firearm...

C. It shall be unlawful for any person supervised by the Department of Corrections or any division thereof to have in his or her possession or under his or her immediate control, or at his or her residence, or in any passenger vehicle which the supervised person is operating or is riding as a passenger, any pistol, shotgun or rifle, including any imitation or homemade pistol, altered air or toy pistol, shotgun or rifle, while such person is subject to supervision, probation, parole or inmate status...

G. For purposes of this section, "sawed-off shotgun or rifle" shall mean any shotgun or rifle which has been shortened to any length.

H. For purposes of this section, "altered toy pistol" shall mean any toy weapon which has been altered from its original manufactured state to resemble a real weapon.

I. For purposes of this section, "altered air pistol" shall mean any air pistol manufactured to propel projectiles by air pressure which has been altered from its original manufactured state.

The specific language restoring the right of a convicted felon to own a firearm, work in law enforcement, and be a gunsmith is located in section B of the same law:

B. Any person who has previously been convicted of a nonviolent felony in any court of this state or of another state or of the United States, and who has received a full and complete pardon from the proper authority and has not been convicted of any other felony offense which has not been pardoned, shall have restored the right to possess any firearm or other weapon prohibited by subsection A of this section, the right to apply for and carry a handgun, concealed or unconcealed, pursuant to the Oklahoma Self-Defense Act and the right to perform the duties of a peace officer, gunsmith, or for firearms repair.

It’s that simple - if you are a convicted felon, you have to go through the Governor to get your 2nd Amendment rights reinstated.