He does seem to appear in the 1900 census , then a soldier, the only one listed in Birmingham at 241 Wellington road, :
John Coopey (38) soldier with Royal Warcks. Born Churcham Gloucest.
Edith J Coopey (29) wife born Kenilworth, Warcks
William J Coopey (5) son born Perry Barr
Arthur G Coopey (6 months) son born Perry Barr
Both he & his wife have ticks in the disability column, but not sure whether these are an artefacts from checking the results (like the lines which sometimes virtually obliterate the information you want ).
It looks like his death was reported the first quarter of 1942, and that he served in the machine gun corps of the Gloucestershire regiment in WW1.
In 1921 there was a coal merchant in Wood lane (Edwin James at no 33) , but it is not listed in 1932. Unfortunately no directories for 1922-1931 are available on CD or online, and this is the period you are really interested in
Mike