William Doherty married Catherine Coyle at Long Tower (St Columb) Roman Catholic Church in 1856. Patrick was another child born 1862, no doubt there may be one or two more.
Wonder if this could be Patrick and William in 1901 (pure speculation at this point)-http://www.census.nationalarchives.ie/pages/1901/Londonderry/Waterside/Dungiven_Road/1540127/