Hawaiian singer Don Ho once said that this episode of I Dream of Jeannie (1965) and the season 4 premiere episode of Hawaii Bound (1972) is what most younger people remember him for.
This is the first of 3 episodes taking place in Hawaii. All three were filmed together, though the third one was broadcast out of order early in the season (#3.3); the first two in mid-season (#3.14 & #3.15).
Jeannie Goes to Honolulu (1967) is the prime proof that Barbara Eden was not obligated by the censors to cover her navel. The likely reason goes back to Season 1. Barbara Eden was pregnant in the first season with the pregnancy post-birth weight and stretch marks being an issue. In this Hawaii episode, Emmaline Henry(Amanda Bellows) ran about the beach wearing low ride jeans and a short top with her belly button clearly showing, for she never had any intention of being pregnant given her LGBT status. And most of the other girls on the beach in bikinis are clearly showing their belly buttons. In the end, this episode depicting an army of naval-showing women affirmed it was Barbara Eden's post-birth appearance that was covered up, and nothing to do with censoring.