Guest Relations, or if you want to get your B-Day button at, or even after midnight, The Pleasure Island Ticket booths have them too. They usually try to keep one or two at the club doors with the ticket/admissions CM's too.
We picked up our DD's at Guest Relations at Magic Kingdom. We were picking up our AP's, the CM read the girl's birthdates and asked if they would each like a birthday pin! They got so much attention and even a free ice cream from one of the carts when we stopped to purchase! They really enjoyed their day!!