Create a white base for the rest of the clown face. If you're applying it to skin, use a cream makeup and apply it liberally with a sponge.
Choose pastel or jewel colors instead of the traditional red. A deep blue or purple can be really cute -- especially if it matches some aspect of the clown outfit. Red can look aggressive or threatening, especially to children, so stay away from a lot of bright red accents if you want to create a cute clown.
Incorporate shapes into the facial design. Instead of a circle around the eye, sketch a star or a heart. Fill it in with the same color you sketched it in.
Create more shapes around the eyes and the mouth of the clown. Extend the lips of the clown up like a smile. Blunt the edges instead of making them sharp, so your extended lips should end in a semicircle.
Emphasize the eyebrows of the clown. Consider making rainbow-colored eyebrows. They'll be friendly and fun to look at.