My son has really sensitive skin, and children's sunscreen is making his skin really itchy. What can I put on it?

Sunscreen. Try using a hypoallergenic sunscreen with no perfumes or preservatives in it. These are the cause of most of the skin sensitivities with sunscreens. There is no magic to "children's" sunscreens, they just have a high SPF. If you can't find a product that doesn't cause problems then consider seeing an allergist for patch testing to see what component he may have a sensitivity or allergy to.
Stop that sunscreen. If one product cause skin problems with your child use another. Look for those that are for sensitive skin. Sun protection is very important.