I have wanted to paint a rug on the staircase going up to my third floor bedroom ever since I bought my old house. Since my idea of painted tiles was pooh-poohed, I figured paint was the ticket.
You start out painting the background color, then the designs (swirls, flowers, whatever) on the uprights > [_ and some on the treads, too. Coat the whole works with a good sealer that will protect the paint against wear.
Sunset magazine, several years ago, showed a staircaser that someone had painted the uprights with plants and fish as tho' it was a giant aquarium; it was GORGEOUS!!
Good luck with your timimg and the kids dilemma!