Air date: 1950s; 1962
The first incidence of on-air nudity (sort of) dates from TV's Jurassic period, and a children's show broadcast in the Detroit area. Lunch With Soupy starred Soupy Sales, and one day during the show's Motown run (1952-60), the crew played a practical joke. When Soupy went to answer the door at the back of the set, a nude woman holding a balloon was there to greet him. As the legend goes, Soupy saw her, and thought her Eisenhower-era pontoons were going out to impressionable youths, but the crew had actually switched the video feed. So, no tits for tots, we're afraid.
Since the show was live, video from that episode doesn't exist. The stunt was recreated in 1962 when the show was in Los Angeles, and that clip is online and totally findable.