Are you staying onsite? They have buttons!
CMs also carry buttons (DS has gotten 2 or 3 honorary citizen buttons from random CMs wandering around, and we got 1st Visit buttons from a Peter Pan CM when we answered "no" to "have you ever been on Peter Pan before?"), and stores, I've read, keep them behind the register as well.
And if you have a character breakfast before you to to the parks, you can tell them your button-needing occasion when you make the Priority Seating, and it should be passed along to the servers so that your family can get them.