
Darigaaz the Igniter |

The other alignment restricted classes (Clerics, Druids, Monks, Paladins) all have a section at the end of their entry about what happens when they change to a forbidden alignment and/or violate their code of conduct. But the barbarian section ends with Greater Rage even though in the opening section it says they must be non-lawful.
Note that I'm working off of a 1st printing Core Rules.

Kenjishinomouri |

The other alignment restricted classes (Clerics, Druids, Monks, Paladins) all have a section at the end of their entry about what happens when they change to a forbidden alignment and/or violate their code of conduct. But the barbarian section ends with Greater Rage even though in the opening section it says they must be non-lawful.
Note that I'm working off of a 1st printing Core Rules.
The PRD says they lose the ability to rage, and cannot level up in barbarian while lawful.

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If you want to go by RAW, once a barbarian becomes lawful he stops being a barbarian, loses all his powers, and there ain't nothing he can do about it. Since Druids and Paladins etc. have explicit options for regaining control, and the Barbarian doesn't, that implies that Barbarians aren't meant to be able to regain their powers once they lose them in this way.
RAI, I'd say an atonement spell would work for them just like it does for the other classes. Becoming lawful is a strange thing to "atone" for, but I can see a CN druid casting it for you.
I can see it now: a noble berserker, tempted by the fruit of city life, finds himself gone soft and returns to his clan to seek forgiveness. The chieftain shows mercy and directs him to the clan's soothsayer to perform the ritual to reawaken the fury that yet lies dormant in his heart.

Ashenfall |

Troll, there is one archetype: it's the "King of Aquilonia" archetype. Unfortunately, you have to be playing in the Hyborean Age, and there's only one wizard in the whole setting. But, with the combined powers of RAGELANCEPOUNCE and OMGWTFBBQIHASAKINGDOM, it sort of mitigates the magic imbalance.
Crom! Count the dead threads!

Ashenfall |

At some point in the comic series, Conan becomes king of a nation called Aquilonia. He became faithful to one woman (his queen), and had a son. It was like Conan started off as a mixture of whiskey, dragon's blood, and diesel fuel, and ended up as a diet wine cooler.
Howard only wrote Conan from '32 until '36, when he committed suicide.
And if Conan was ever anything other than a barbarian, it would have been a rogue. He never got into soldiering or wearing heavy armor; at most, just a light chain muscle shirt.