National Archives Soldiers and Sailors System lists a John Dinan as member of the 79th New York Infantry. Roster put together by NY Adjutant General does not list any John Dinan in the 79th NY but does list the following:

DINERE, JOHN.—Age, 20 years. Enlisted at Brooklyn, to serve three years, and mustered in as private, Co. A , August 12, 1864; mustered out with company, J u l y 14, 1865, at Alexandria, Va . ; also borne as Dinen, Dinan and Dinnan. This would not seem to be your man.