From Fred R. Shapiro's piece about his Yale Book of Quotations, in The Chronicle:
"Boola Boola." The usual attribution of authorship of this quintessential Eli fight song is A.M. Hirsh, Yale Class of 1901. There are, however, alternative theories. To begin with, it needs to be noted that the Yale song was adapted from an 1898 song by two African-American entertainers, Bob Cole and Billy Johnson, titled "La Hoola Boola." In addition to the "Boola" title, the melody is virtually identical to the earlier song. When the Yale "Boola" song was published in 1901, it had the notice, "Adapted by permission of Howley, Haviland & Dresser." Howley, Haviland & Dresser was the publisher of "La Hoola Boola."
Over the years, some have questioned whether Hirsh was the real adapter. In 1905, Charles H. Loomis, the song's publisher, asserted in the course of litigation with Hirsh that Hirsh's name had been listed as composer as part of a contractual arrangement to promote the song, which had actually been adapted by Loomis himself from "an old song" and which "Hirsh had no more to do with than the man in the moon." The suit was subsequently settled.
In Hawaiian-music circles, it is widely believed that the Hawaiian musician, orchestra leader, and businessman Albert R. (Sonny) Cunha wrote the Yale Boola song. When Cunha died in 1933, The New York Times and The Washington Post both memorialized him as one of its composers.
When I look through the volumes of the Yale Alumni Weekly for 1900 (when the song was first mentioned) and the years thereafter, however, I see that authorship of the song is routinely ascribed to Hirsh. I have found no solid corroboration of the claims for either Loomis or Cunha, so, in the absence of further evidence, Hirsh's claim still appears to be secure, albeit surrounded with some question marks.