I stumbled across a listing for a golf club named the David's Island GC. David's Island is a small 78 acre piece of land located just off of Westchester County in the Long Island Sound. The island was home to a Civil War hospital and became know as Fort Slocum some time after the war ended.
The military history of the island is a good read, including its time as a staging depot during WWI and its later use as a Nike Ajax base.
Some time around the turn of the century (c. 1900), there was a golf club on the island. I have no idea what the state of the playing field was for this club, and whether or not they actually played any golf on the island. But the history of officer's clubs establishing rudimentary courses on the parade grounds or other suitable land of a military base suggests that golf became a pastime for those stationed "offshore." It is also entirely possibile that the club was just that, and engaged in its golf activities at some of the courses on the mainland (there were several courses taking root mere miles away).
If anyone has any information on this club, I'd be interested in hearing the updates.
Sven