I always think of this line as the famous Kings. Not only will you find them in the publications I mention in the text, but also in various other publications, such as Who's Who and the Encyclopedia of American Biography, available at most libraries. I imagine if you looked in early New York City newspapers, you would find most of their marriages and births and deaths as well.
The descendants of Charles King of Maine are in the Ancestral File, but he is not tied to his father, John King. I wouldn't be surprised to find additional members of the family in the Ancestral File, as well, since Eleazer King and family were apparently early members of The Church of Jesus Christ of Latter-Day Saints (Mormons).
One thing I should mention, however, is that I had a really hard time trying to find them in the U S census records, and I wondered if part of this was due to the fact that a lot of them spent quite a bit of time out of the country as ambassadors and such.
I would like to hear from anyone who has additional information about descendants of this line of famous Kings.
First Generation
Second Generation
Third Generation
Fourth Generation
Fifth Generation