I screwed two white cup hooks into the underside of some white molding along an archway in our kitchen. When I remove the hooks, the holes won't even be visible.
(I realize that not everyone has an archway exactly like this, but look for other possibilities that might work. For example, I did the same thing under the mantel to hang up seasonal decorations. The underside of laminate countertops/bars works well also.)
Purchase small curtain clips similar to this one. They are available at Ikea and at numerous online sources:
Using clear fishing line or sturdy string that blends into your wall color, tie one end of the string to one of the hooks, add the curtain clips, and then, keeping it taut, tie the string to the other cup hook. I used white kite string, and it is almost invisible.
Let your budding Picassos and Da Vincis hang up their art treasures--and enjoy.