What's a good sunscreen for children with very sensitive skin?

My two little daughters have very fair complexions. Because of this, they don’t go out in the sun during the summer because they burn easily. We’ve tried different sunscreens, but because of their tender sensitive skin, they react badly to them——skin irritation and inflammation. It seems the combination of sunscreen and sunlight triggers the reaction. Having such sensitive skin spoils our family outings every summer. Their mother has a fair complexion too, but she can take the regular sunscreen products. As for me, I have a naturally “tanned” complexion, but I still use sunscreen, and I don’t have any problems with it. Is there a sunscreen product out there for children that provides effective sun protection without the irritation?