What kind of mosquito repellant would you recommend for newborns? Is there anything that's safe to use on the skin?

You may consider getting mosquito repellent patches which can be pasted onto the child's clothes and are just as effective. It's like a scratch and sniff pad where the pad releases natural oils to prevent mosquitoes from coming near your baby. You can purchase them at AgapeBabies: http://www.agapebabies.com/agapebabies/disney-winnie-the-pooh-mosquito-repellent-patch-24-patches.html