Thanks to Hesham for finding this article.
As a consequence I went to the book United States Naval Aviation 1910-1980 (published by US Govt Printing Office, 1981) and found the following references in the chronological report:
(p.9) 30 August 1913: A Sperry gyroscopic stabilizer (automatic pilot) was flight tested in the C-2 Curtiss flying boat by Lt (jg) P.N.L. Bellinger at Hammondsport, NY.
(p.15) 12 September 1916: A demonstration of guided missile equipment - a piloted hydroaeroplane equipped with automatic stabilization and direction gear developed by the Sperry Company and P.C. Hewitt – was witnessed by Lt T.S. Wilkenson of the Bureau of Ordnance at Amityville, Long Island. Wilkinson reported; “The automatic control of the aeroplane is adequate and excellent. The machine left the water without difficulty, climbed to its desired height, maintained this attitude until the end of the run, when it dived sharply, and, unless controlled by the aviator, would have dived to the earth”.
(JH: There is no reference as to the type of aircraft used)
(p.25) 14 April 1917: The Navy’s first guided missile effort began when the Naval Consulting Board recommended to the Secretary of the Navy that $ 50,000 be apportioned to carry on experimental work on aerial torpedoes in the form of automatically controlled aeroplanes or aerial machines carrying high explosives.
(p.29) 10 November 1917: A Navy ‘flying bomb’, manufactured by the Curtiss Company, was delivered to the Sperry Flying Field at Copiague, Long Island, for test. Also called an aerial torpedo, the flying bomb was designed for automatic operation carrying 1,000 pounds of explosives with a range of 50 miles and a top speed of 90 miles per hour. In addition to this specially designed aircraft, N-9s were also converted for automatic operations as flying bombs that were closely related to the guided missile of today.
(JH: There were thus two different types of aircraft. Curtiss built 120 N-9s and Burgess another 60, so identifying which aircraft were used in this programme is not feasible. As far as the other type of aircraft, perhaps somebody can look it up in books on Curtiss aircraft)
(p.30) 21 November 1917: A demonstration of the Navy N-9 flying bomb at Amityville, Long Island, was witnessed by Maj. Gen. George O. Squier, USA, Chief Signal officer. Subsequently the Army established a parallel aerial torpedo project.
(p.31) 6 March 1918: An unmanned flying bomb type was successfully launched and flown for 1,000 yards at the Sperry Flying Field, Copiague, Long Island. The launch device was a falling weight type catapult.
(JH: On p.43 of this book is a tiny photo similar to the ones provided in the earlier article)
(p.34) 23 September 1918: The flywheel catapult, a forerunner of those later to be installed aboard the Lexington and Saratoga, was used successfully to launch a flying bomb at Copiague, Long Island. Development of this catapult by the Sperry Company had been undertaken in connection with the Bureau of ordinance flying bomb project.
(JH: One of the photos provided in the earlier article of the flying bomb on the top of a car, seems to be an additional test)
(p.35) 17 October 1918: A pilotless N-9 training plane, converted to an automatic flying machine, was successfully launched at Copiague, Long Island, and flew a prescribed course, although the distance gear failed to land the airplane at a pre-set range of 14,500 yards. The plane was last seen over the Bay Shore Air Station at an altitude of 4,000 feet, flying eastwards.
(JH: I do not have a record of an N-9 having been written off on 17 October 1918)
There are no further references to this project in 1919 and 1920. I did not check beyond that year.