The Albany City directory of 1940 has a John Cunningham (longshoreman) and a John Cunningham JR (laborer) living at 246 Hamilton. In 1941 and 42 it is just John Jr. at that address, see attached.
Edit: In case you ask, according to the Albany directory abbreviation page: "NYC , WA" means "New York Central & Hudson River Railroad Co., West Albany"
Looks like JR was the one born 1910, so... if there is a father John and son John Jr at 246 Hamilton in 1940 how can it be the one you're looking for? You wrote that his father was named Patrick.