Short answer
A tiny, rice-sized dab of coconut oil is generally safe for a puppy, whether applied to the skin or given orally, but it's important to be extremely conservative. Puppies have very sensitive digestive systems, and even a small amount of fat can cause greasy diarrhea or an upset stomach. For internal use, start with a minuscule amount and wait to see how their tummy handles it. It's always best to consult your puppy's vet before introducing any new food, even something generally considered safe.
Coconut oil — Food safety facts
Safe to share · Dogs · full breakdown on the linked food page
Safe in very small amounts. Too much causes greasy diarrhoea.
The full verdict, portion guidance and serving notes are collected on the Coconut oil food facts page.