What to do:
Set up the challenge on one of your library's blogs (I recommend Tumblr since it is very easy to post photos). Each week set the "color" challenge i.e. 'This week read something RED'. Have teens submit photos of book covers they are reading for the challenge. Simple, easy and reading based!
When you are finished you can use the images submitted to create a color wash "Reading Quilt" just for the teens at your library. You could even go WAY over the top and have the covers printed on cloth and make them into a physical quilt to raffle off or give away as a prize to one of the participants.
Here's an example of a digital "Reading Quilt" using book cover art from titles mentioned on this blog: