Mix the flour, oil, cream of tartar and salt in a medium saucepan. Turn the burner to medium-low heat. Slowly add 2 cups of water. Cook and stir until all the ingredients blend together and the dough is stiff and dry, about 5 minutes. Pour the dough out onto wax paper and let cool.
When cool, knead the dough until smooth and feels like play dough. Separate the dough into 3 sections. Wearing plastic gloves, add 4 to 5 drops of food coloring to each section and knead until the color is incorporated. Store the play dough in an airtight container.
Use beet, spinach or carrot juice as dye alternative. If play dough dries out, add water.