How do I unlock the region code on my PS2?

May be...

Not for DVDs, though. I bought a game in Japan and I can't play it because, yep, it's region locked. I really really want to play this game or else it would have been a waste of money. So what do I do?

Purchase SwapMagic kit or install a modchip.

You'd have to either mod the system, or get someone else to. The PS2 wasn't meant to be "unlocked" as far as just going in to the system and doing it yourself.