Found a list of suggested products for children that are DEET free, that would be the way I would go, gentle and made from plant oils for the most part.
Avon Skin So Soft Bug Guard Insect Repellent
OFF! Botanicals Plant Based Insect Repellent (oil of lemon eucalyptus)
Cutter Advanced Insect Repellent (Picaridin) (Picaridin is another chemical ingredient found in repellents and is not a natural product. It is thought to be as effective as DEET and can be another option for parents looking for an alternative to DEET to consider.)
Bull Frog Mosquito Coast
Burt's Bees Herbal Insect Repellent (Lemongrass Oil, Citronella Oil, Rosemary Oil)
California Baby Bug Repellent Spray with Citronella
Repel Plant Based Lemon Eucalyptus Insect Repellent
There is probably a similar list for adults.