eliminating the men in the 1956 City Directory using the 1950 census. - Which is free on ancestry.com to us here in the U.S. - It might be worth a try from the UK.
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James C Reilly in Dedham
1950 Census says he was born in Massachusetts and never married. is living with a brother John E Reilly and his family. was a repairman for trains, on the railroad
James R Riley in Walpole was born about 1920 in Massachusetts. is married to Jean M and has a 2 year old daughter born im Massachusetts. was a machinist for the railroad
James J Riley, Jr sub[way?] foreman MTA, home at 19 Salem Place, Malden - didn't find a good match for him, but the 3 that came closest were all born in Massachusetts.
James P O'Riley resides 16 Concord Sq - could be the man on Newbury Street by that name. born in Massachusetts in 1901, never married, is a government clerk
James F Reilly - there were 6. all were either married or were children except 1 who was born in 1870. all were born in Massachusetts
That left the two without middle initials. For them I looked for James Riley born in Ireland (exact) and living in Boston (exact). This would have turned up "your" James anyway, if he was there. There really isn't a good match. The only 2 that came close are both much older than being born in 1914:
James Reilly, 53, married, born in Ireland, in the Boston State (mental) Hospital. probably not him since it is hard to get hit by a trolley in the state hospital.
James Rahilly, 67, widowed, born in Ireland, a car cleaner for the railroad. in the household are two sons Morris and Donald, 25 and 34, born in Massachusetts.
living on Berkeley St, Boston.
too old if your James was born about 1914. otherwise he could be a match if he started another family in the US.
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When were his children born? That would at least give us an idea of how long he stayed in Ireland and when he was born.