Another great idea inspired by Pinterest!
I bought solid colored plastic table covers and shower curtain rings at the dollar store.
Before completely unfolding the table covers, I cut them into 2" strips using a rotary cutter and ruler. They were knotted in rainbow order around the rings. I tried gluing the first couple to keep them in place and then decided wasn't really necessary.
Total price was $8 for 24 rainbow rings.
They were strung around to decorate for the party and the guests were each given a "rainbow" as a party favor.