“The game was stopped while Detroit was batting in the sixth, Cleveland claiming that a ‘rabbit’—a lively ball with more rubber than the law allows, had been rung in.” Detroit Free Press, April 27, 1906, p10
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1907. “The Cleveland camp followers, when Macon won on Wednesday, went to the old family chest and brushed the moth powder off the ‘rabbit’ ball story that was sprung a dozen times during the championship series a year ago” (Joe S. Jackson, Detroit Free Press, March 31; Peter Morris).