I found three cites that attribute its coinage to Dr. John Wilce, a football coach and professor of clinical medicine at Ohio State University. Wikipedia
(I know, I know, but bear with me) dates its first public use to a lecture he gave in 1916; in his paper, "Jacques and the Fat Man: Physical Culture and the Abdomen in Modern France"
(warning - PDF file), Christopher Forth, of the Australian National University, cites its first use "by John Wilce sometime after 1913", and in American Speech, Vol. 30, No. 3 (Oct., 1955)
, Tom Burns Haber said, "the euphemism has been in existence for about four decades", which would place its first use around 1915.