Using hot wax with children would be risky, so I have checked out several alternate methods. Some people use gel glue in place of the wax, but I have found that to be difficult to wash out of the cloth. Here is the method that I used for the pictured example:
Supplies: cotton fabric, squeeze bottle, flour, water, acrylic paint and/or fabric dyes
Directions: Mix flour and water to the consistency of pancake batter. Use a funnel to transfer mixture to your squeeze bottle. Place your fabric on a sheet of foil or cookie sheet since the flour and water will soak through the fabric and you will want a stable surface to move your piece so that it can dry overnight. "Draw" on the cloth with your flour mixture. Dry. I then covered the entire background with the light green acrylic paint, dabbing it on with a sponge. Before that dried, I used the little bottle of spray fabric paint to add some bursts of color. After the paint dried I rinsed away the flour with hot water and ironed the fabric. The result is slightly stiff, I imagine because of the acrylic paint, so the finished piece would work well as a wall hanging as opposed to turning it into something to wear. However, I imagine that if you were to stick with fabric dyes it would be much softer to the touch.