I am not familiar with the Royal Stables, however Kansas City, does or did have a horse and livestock show that is held yearly known as the American Royal since the 1930's. Members of the Kansas City Club, developed a Riding Club in KS known as The Saddle and Sirloin Club. It housed stabled roughly 133 horses, and provided living space for the horse hands. If you have a photo, I would be able to confirm if it is the same grounds, which I bet it is. I worked at the club from 1991 to 1994, in the clubhouse as a catering manager. There is also Benjiam Riding Stables which is open to the public and still in operation located on the MO side.