The Rainbow Piece is a new item for the Saint Patrick's Day update. It is comparable to the Fallen Star, but instead of falling in the night and exploding at dawn, it falls during daytime and explodes at dusk. Once you have collected at least 5 rainbow pieces, you can then craft the Pot o' Gold by hand.
You can find rainbow pieces anywhere, as long as it is daytime outside. You can make a rainbow piece farm by making a huge rectangle with no roof and waiting for some rainbow pieces to land inside. The bigger the rectangle is, a better chance of getting the rainbow pieces comes to you.