I know this post is a year old. Yet a book on Gene L. Coon has been finished after several months of research and is undergoing end stage prep. As far as living relatives, Jackie is supposedly still alive. She married a politician named Ben Fernandez after Coon's death. Widowed again in 2000. She may have a stepdaughter named Kathleen. Coon had at least two brothers, nothing is known of what became of them. He may have fathered a child, again nothing is known. He also has some cousins still living in Beatrice, Nebraska (his hometown). No contact info on them. There may never be a complete biography on Coon in the personal life/family sense.
However, a treasure trove of stuff was discovered through the archives of The Beatrice Daily Sun, various Trek publications, and The Los Angeles Times. Interesting how Star Trek (especially Season 3) seems lost without him. After It Takes A Thief and his attempt at producing The Name of The Game, he largely returned to being a jobbing TV writer in his final years. So, in a sense, he was lost without them also. Roddenberry and Coon both sort of jobbed around (Granted, Roddenberry created The Lieutenant and Coon did films such as The Killers. Also, Coon's early involvement with The Munsters and McHale's Navy). until Star Trek. A listing of his papers from The University of Wyoming will also be included. Not only was he involved in The Questor Tapes, but also Genesis II and the concept for Roddenberry's pilot/TV Movie Spectre. Airing a few years after his death. And yes, the U of Wyoming papers verify it. They also reveal he did in fact write an unfinished 38 page memoir on his time on Star Trek.