From her husband Bill Bumpus, Gayle King has a daughter and a son named Kirby and William Bumpus Jr. However, there is no further information about her children in any of the mainstream.
According to the mainstream, it seems like she likes to keep her personal information far away from the public which is right of her decision as well.
Being a celebrity, Everything that must be needed for the public isn’t good as well, some of the family information must have to be kept in private which is safe for everyone as well.