Well, maybe not so clean, but it is fun. I'm sure you remember making salt dough - it doesn't get more economical than this:
Salt Dough
2 cups flour
1 cup regular salt
Approximately 1 cup water
Mix the flour and salt together and add enough water so the dough is neither too wet or too dry - it should be smooth. Knead for 10 minutes. Garlic presses, cookie cutters, toothpicks, etc. are fun for shaping. If needed, use crumpled aluminum foil to prop up the masterpieces. When ready, you can let your creations air dry or you can bake them in a 200 degree oven for 1 - 4 hours.
I know, I know, not too wet or too dry, 1 - 4 hours...those kinds of directions drive me nuts, but the amount of water really depends on the humidity and the baking time on the size and thickness of your creation. When baking, take care to not get them too brown (they will crack) and if a bubble pops up you can use a pin to deflate it.
After baked, they can be painted with acrylic paint. If it is a real "keeper" you can apply a coat of finish. You can make your own economical version by mixing 1 tablespoon of water with 1 tablespoon of Elmer's glue. I happen to have a container of Minwax Polycrylic that I picked up at our grocery super-store. It is not so economical at $5.99 for 8 oz, but is really great for other projects too - it dries quickly, doesn't smell too bad and is easy to clean up.
So, there you have it - an inexpensive project that will keep the little guys busy (okay, I may have kept myself busy making a few) for quite some time. So go make some magnets, beads, ornaments, pins...