Firstly, I hope it's the Hal Gordon Green Lantern.
Secondly, well...good luck getting rights to anything from the Big Two (Marvel or DC) as I'm sure with the recent spate of super-hero flicks, most more well known properties have likely already been all snatched up. Plus, it'd probably cost you a small fortune.
As for writing your script, sure, you can write anything you want. Just don't try to sell it without rights/approval/etc.
What I'd do is query DC to pitch your idea to them. If you manage to somehow impress the hell out of them with your pitch and they say, "Yes, write us a screenplay!" then bully for you. Conversely, if you write the screenplay, pitch it and they turn you down (which will likely happen as The Big Two very rarely work with anyone save for established screenwriters) then you've written the screenplay for nothing, unless you're the "glass is half full" type and could always just consider your script as practice.
Sorry if I burst your bubble, but...yeah...DC in the big leagues and you'd have to REALLY amaze them for them to even consider it.