Play Out the String (1878)

“He wished, further, to say that the newspaper talk about the disbanding of the Indianapolis team was utterly without foundation; it would ‘play out the string’ on schedule time, whether in St. Louis or Indianapolis, and all agreements would be met.” Chicago Tribune, June 29, 1878, p5

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1912 (New York Tribune, Sept. 15; Edward J. Nichols).