Homer (1868)

‘[English cricketers vs. Union of Morrisania 10/20/1868] In the fourth innings the cricketers made five runs on good hits, Willisher hitting clean for a ‘homer.'”  New York Clipper October 31, 1868 [Richard Hershberger]

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1875. “By [Lipman] Pike’s error a first-base hit was changed to a ‘homer’” (New York Clipper, July 24; Peter Morris).