I Dream of Jeannie (1965)

Air Force captain Anthony "Tony" Nelson is stranded on a desert island after his space capsule malfunctions on re-entry. While he is there, he finds a bottle and upon opening it he releases a beautiful genie named, coincidentally, Jeannie who was trapped in the bottle by the evil Blue Djinn. Eventually, Tony is rescued and he brings Jeannie back with him. The only other person who knows of her existance is Tony's best friend, Army captain Roger Healey. Tony tries to keep her existance a secret from Air Force psychiatrist Colonel Alfred Bellows and his wife Amanda and he is successful for a few years until he asks Jeannie to marry him. He then reveals Jeannie's existance, but not her powers, to the world.