Spin each blindfolded participant around three times, then point them toward the big paper rainbow, with a personalized sticky-backed pot of gold in hand. Whoever places it closest to the end (or ends) of the rainbow wins. Change the game to Pin the Hat on the Leprechaun if you'd rather!
Right before the party, hide gold foil-covered chocolate coins outside or inside, depending on weather and space considerations. Plan for roughly a dozen coins per guest. If you have a mix of older and younger kids, consider marking coins hidden in lower, easier spots to designate them off limits for the older set. Send each kid hunting with a personalized paper bag in hand. Bonus: Make decorating this bag with stamps and stickers a pre-hunt activity. Or, toss a few extra St. Patrick's Day-themed goodies into each guest's bag as he or she leaves.
Gather the kids in a circle, either seated or standing. Whether you use a beanbag, soft ball or an actual potato, tell the kids to pretend it's very, very hot, so pass it on as soon as possible. (Decide beforehand if it should be passed around the circle in an orderly fashion or can be tossed to anyone.) Have someone, with back to the group, in charge of playing Irish music on a CD or iPod, then stopping it at random points. Whoever's holding the potato when the music stops is eliminated. The person left standing at the end gets to be in charge of the music during the next round.
