Listening to Party Animals OSTs on youtube, I don't feel like there's one that sounds like a birthday theme. I guess for there to be one there would have to be a stage with that theme. I don't think it's possible that they would take that into account as a suggestion for a special thematic stage in quick play... although there could be a winter cabin type stage with a birthday OST (Original Sound Track).
Sorry if the text is confusing because of Google Translate.
