So sorry for my vague replies earlier. I have received a list of internments from Green - Wood and on the grave and the internment documents it clearly states the name as Johnston for Robert.
The relatives in the grave along side him are as follows

Robert Johnson 1814 - 8 Apr 1885
Bridget McGurk Johnson 1810 - 14 July 1873
William Henry Johnson 1849 - 15 Sept 1902
Margaret Johnston Kennedy 28 Dec 1848 - 24 July 1924

William and Margaret being children of Robert and Bridget.



As you can see from the dates.. Robert Johnston born 1862 doesn't really fit as a possible child to William or Margaret. He possibly could be the son to Robert and Bridget but seems very unlikely, Bridget would have been at least 52 at the time of his birth.
The boroughs i have searched in NY are : Bronx, Brooklyn and Manhattan
The letters i received stating no records found was from the Municipal Archives in NY.
I really had high hopes of finding out who this little boy was and who his parents were, but just cant seem to find out anything.