Not to be confused with a trading pin, I'll refer to these as buttons.
You can stop in at City Hall and ask if they have any, however they were so popular the first week they were out, that I believe City Hall has reverted back to stickers. They had First Visit, Birthday, Honoraray Citizen, Just Married, Anniversary and Family Renunion buttons. It may just be the birthday buttons that have gone back to stickers though.
You'll have much better luck (and shorter wait) if you find one of the Dream's cast members. They all carry a small supply of the buttons. When I went with my parents and my son last month, we all got a button. I think I got Honarary Citizen and so did my son, my parents each got an Anniversary button, and my dad got a Happy Birthday in Spanish (Feliz Complanos?? sorry I took French in school) just because the CM didn't have any more English ones.
Look for Jerry, he's a hoot. I've ran into him on a few trips now.
Oh, and they are not specifically YOAMD buttons, but they became available when YOAMD kicked off.