Yes. It's possible to paint with food - and kids love it. They enjoy the whole process, so allow them to be hands-on and involved in the whole process.
You'll need: food coloring and eggs (the same amount of eggs as bottles of food coloring), watercolor paper and/or a bar of white chocolate, brushes and optional permanent marker.
Separate the egg yolks from the whites - put each yolk in a separate dish. Put a few drops of one food coloring into a yolk dish and mix the yolk and color together. Then repeat the process with the remainder of the yolks and coloring. Now you have a basic (and edible!) form of egg tempera. You can also mix some food coloring with the egg white - it's turns out more transparent but is still interesting. Now you can simply take some watercolor paper and let the kids get creative! If you want a little more structure you can use a permanent marker to make a shape and color the different areas with different colors. This gives a great stained glass window effect.
If you have a bar of white chocolate you can paint the chocolate - with patterns on the patterned side, or a scene on the full back. This is a great activity for a chocolate-themed birthday party! The chocolate is actually edible (within a few days as long as you keep it refrigerated).