There's rings for about every color in the Rainbow, but no Beige. Okay, here it goes:
It would be unknown what beige represented, though Jazzimus would've had the ring. Despite being an Flame and Sigma, it thought that he was worthy (Thor logic again..). I guess you already have to be Uber-powerful,like almost Superman-levels of powerful (LITERALLY DRIPPING POWER.) to be a Beige Lantern, but this is simply a hypothesis.
I would've gave the ring to Kanye West but he'd probably be a rainbow lantern as he basically could have all the known traits.