The phrase "Ivy League" has a complex history without a clear origin date or attribution.

The New York Herald Tribune used the term "Ivy Colleges" first, in 1933 by a reporter named Stanley Woodward. The term Ivy League was formally adopted by Princeton, Yale, Harvard, Columbia, Penn, Dartmouth, Cornell and Brown in February 1954 to describe their alliance to play each other in sports. Footnote 1

Brown University cites an earlier article as the first using the term "Ivy League:" "In February 1935, Associated Press sports editor Alan Gould wrote, “The so-called ‘Ivy League’ which is in the process of formation among a group of the older Eastern universities now seems to have welcomed Brown into the fold and automatically assumed the proportions of a Big Eight.’” Footnote 3

Dartmouth College history professor Jere Daniell, has studied the issue and his attribution is to Caswell Adams, also a sports writer for the Herald-Tribune. His reference is as follows, "In 1937,  Adams is rumored to have complained to his boss about having to write about those old “Ivy-covered” universities and in his article about the Columbia/Penn game coined the term “Ivy League.” Footnote 2 

Sometimes the phrase "Ancient Eight" is used to refer to Ivy League schools. The term Ancient Eight was first used in reference to the first eight professional baseball teams: the Boston Red Stockings, Chicago White Stockings, Cincinnati Red Stockings, Hartford Dark Blues, Louisville Grays, Mutual of New York, Philadelphia Athletics and the St. Louis Brown Stockings.

The first reference to the Ancient Eight regarding the Ivy League schools was in the Ithaca Cornell Daily Sun on November 21, 1951, when they wrote, "Charley Caldwell's Tigers, well on their way to capturing the pennant of the Ancient Eight, lead in almost everything else, with Kazmaier being the chief executioner." Charley Caldwall was the coach of the Princeton (Tigers) and Kazmaier was Heisman Trophy winner Dick Kazmaier who played for Princeton's football team in 1951."

So it seems like the 1930s saw the term Ivy League evolve and 1951 is the first reference to the Ancient Eight.

Footnotes:

1. Princeton University Library: https://blogs.princeton.edu/mudd/2015/07/the-origi...

2. Badger Herald: https://badgerherald.com/news/2003/03/03/origins-o...

3. Brown University: https://www.brown.edu/Administration/News_Bureau/D...