I usually look for people in directories for their occupations pre-census records, but there were many John Davisons in the 1831 census (and this is only for parts of Londonderry). Wives and children only by numbers, not names.
I still think that his marriage is your best bet, along with his son's baptism.
My Graham ancestor was one of the troublemakers sent from Scotland to Fermanagh in the 1600s, and I managed to trace his descendants through deeds and MIs, but this was easier because they owned some land. My gt gt grandfather "returned" to Scotland in 1815.
Try a google search for "nailers ireland 1800?" (without the inverted commas) - there is at least one book online.