"Beaver" is the nickname of the City College of New York's sports teams. New York, historically, was a center of the fur trade. Beaver pelts made John Jacob Astor a rich man. You can find beavers decorating the Astor Place subway station.
I'll leave the "Leave it to Beaver" jokes for another day.
14 September 1934, New York Times, pg. 32:
NEW GRIDIRON DEAL
SCORES AT C.C.N.Y.
The Beavers, as C. C. N. Y. is to be known henceforth, will have most of their line strength on the ends of the line.