CMs give away buttons to guests. Our DD received several from the boat captain going from GF to MK. We were the only passengers, mentioned it was her 1st trip to WDW, how excited she was, etc. Her 1st visit button is for all of WDW, not just one park. Not sure that ones exist for specific parks. The best way to get buttons is to be polite and strike up a conversatoin w/ a CM, especially when there aren't lots of other guests around or they're not in a hurry.
Good luck!