You won't need their birth certificate. Children don't need ID. It might not be a horrible idea to bring it - but we've flown with my kids several times - and my son is Korean while the rest of us are white - and no one has said boo.
You WILL need something to keep them occupied on the plane - cd players, books, crayons, gameboys, a portable DVD player, Polly Pockets (although I wouldn't brave all those little pieces on a plane - one of my girlfriends does), travel games, whatever. You'll want some snacks - because a tiny bag of pretzels don't go over well with that set - and maybe haul along your own 20 oz bottle of water or pop. Gum for takeoff and landing (they don't sell it at airports).