If you do a search for Nehemiah John Coyle on Ancestry you will see that a user, pcoyle22, has him on their 'Coyle Family Tree'. It's a Private tree so you would have to send a contact message to them.
They have him born in 1911 in Tonypandy, Glamorgan, which at that time was part of the Pontypridd Registration District.
GRO records show that he married:
Elizabeth M Thomas in 1936 Qtr 1, in the Pontypridd area
Ann B Cleland/Fee in 1964 Qtr 3, in the Coventry area
He died in Feb 1988 in Coventry, Warwickshire, England and his date of birth was given as 21 Nov 1911. However, the GRO index suggests that the birth was not registered until 1912 Qtr 1.
As he was born after the 1911 census you will not find him on any census records.
Was he a full-time soldier or a WW2 conscript? I think you need to try to get hold of his army service record? The military records on-line tend to be only for those who died during the war. So you would probably have to go for the original records.
You might also be able to find him in Electoral Rolls? I can't see a Nehemiah, but there are lots of John Coyles in Middlesex at that time!