Now they recommend:
"For babies under six months of age, sunscreen may be used on small areas of the body such as the face and the back of the hands if adequate clothing and shade are not available. For older children, test the sunscreen on the baby's back for a reaction before applying it all over. Apply carefully around the eyes, avoiding the eyelids. If your baby rubs sunscreen into her eyes, wipe the eyes and hands clean with a damp cloth. If the sunscreen burns her eyes, try a different brand or try a sunscreen stick or sunblock with titanium dioxide or zinc oxide."
There are two very important reasons for not overusing sunscreen in young babies:
1. Infants and children have what is called a high body surface to volume ratio. What this means is that proportionately babies have more skin for the size body as compared to an adult. Sunscreens are made of chemicals. On the older child and adult, the chemical exposure is relatively minimal because the body surface ratio is smaller than a baby. Therefore, babies get a higher "dose" of sunscreen than do those older. While this exposure would most likely not cause any problems, the likelihood of an adverse reaction is greater.
2. Babies have a mildly impaired mechanism to keep cool by sweating. In addition, they have a greater risk of becoming dehydrated due to heat. Sunscreen can somewhat impair effective cooling by perspiration, so placing it on an infant could be detrimental.
A hat and a shade, just thin cotton clothing so their skin can breath well 
