Hello. Long time lurker and fellow sumo fan. Somehow this is the topic that motivated me to make an account.
As the comments have stated, the term "stable" as used for wrestlers, boxers, and actors has been around for some time. A cursory bout of research reveals in Google Books that the term "sumo stable" was used as early as February 1965 by "Black Belt" Magazine: https://books.google.com/books?id=B9kDAAAAMBAJ&lpg=PA63&dq=sumo%20stable&pg=PA63#v=onepage&q=sumo%20stable&f=false
Wikipedia states that Black Belt is one of the longest-running magazines in the U.S. dedicated to martial arts: https://en.wikipedia.org/wiki/Black_Belt_(magazine)
Not a particularly thorough answer but hopefully gives you some perspective for how long the term has been around. My guess is that martial arts enthusiasts in the U.S. (such as the contributors to Black Belt Magazine) started using the term "stable" as an imprecise but rational translation in the mid-20th century, and it obviously grew in popularity until its ubiquity today.