“The managers, directors, ground keepers, bat boys, players, and in fact every one else who has anything to do with the Polo grounds, smiled a very large smile yesterday.” The Sun [New York], May 18, 1887, p4
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
“A little son of Second Baseman [Pug] Bennett acted as bat boy for the cardinals. He is four years old, was decked out in a regulation uniform, and made a particularly fetching figure as he walked out solemnly after each bat” (Chicago Tribune, May 11; Peter Morris).
