I use Caran D'Ache Neocolor II water-soluble wax crayons. They are easy to use and not nearly has messy as actual paint.
My family bought a set of the crayons over two decades ago, and we haven't had to buy another yet. You can buy smaller sets (10 colors) or ridiculous sets (126 colors). They are super fun.
To use: Dip one end in water (warm water will make the person happier). Blot on a paper towel so that you do not drip on the person you are going to paint (the crayon needs to be wet to draw, but not dripping or it will smear the drawing). Draw on person. You can easily blend colors by drawing over an area you already colored, and if you make a mistake you can just put a little water on the area and then wipe it off with a paper towel. Don't forget to remove the drawings from your skin before going to bed!