Apply frequently around the eyes, avoiding eyelids. Children tend to rub their eyes, and stinging could be a problem. Reapply frequently and liberally, particularly after swimming or sweating. Pass up heavily scented sun-screens to avoid attracting insects to your child. Consider applying a zinc oxide product as added protection to such prominent areas as nose, cheeks, top of ears and shoulders.
Zinc oxide is a non-irritating and very effective sun block.
Sunscreens are not intended to increase sun exposure time but to increase protection during unavoidable exposure.