There’s a death that fits your information for an Arthur Dugan registered in Coleraine Oct – Dec 1881 Volume 1, page 301. Estimated year of birth 1803.
Likewise for the man who might be his brother. Isaac Dugan, death registered Coleraine 1866, Volume 16, page 279. Estimated year of birth 1804.
For Arthur’s wife Jeanne, there are 3 possible deaths registered in Coleraine: for a Jane Dougan, 1793 – 1867; Jane Doogan 1801 – 1866 & Jane Dugan 1812 – 1873 Volume 16, page 314. (The names Jane & Jean are interchangeable, and the spelling of the surname will vary according to the whim of the person recording the information).
There’s an Arthur Duggan recorded in Griffiths Valuation for 1859 which states he had a house, offices (outbuildings) and 2 yards in Bellhouse Lane, Coleraine (plots 6 & 7). Can’t say whether that’s your family.
The 1831 census for Ballywoolen has 5 Duggan households (Isaac, James & Neil plus 2 Arthurs).
In 1859, Griffiths for Ballywoolen records Neal Duggan with a farmhouse, offices (outbuildings) and 104 acres (plot 1); Mary Anne Duggan (probably a widow) with a farmhouse, outbuildings and 49 acres (plot 2); Isaac Duggan senior with a farm, ourtbuildings and 32 acres (plot 4); Isaac Duggan junior with a corn mill, kiln and 12 acres (plot 5) & Arthur Duggan with a farm, outbuildings and 18 acres (plot 6).
4 Dugan households still there by the 1901 census:http://www.census.nationalarchives.ie/p ... n/1516988/http://www.census.nationalarchives.ie/p ... n/1516982/http://www.census.nationalarchives.ie/p ... n/1516989/http://www.census.nationalarchives.ie/p ... n/1516990/
3 of the families were Presbyterian, the fourth is Church of Ireland. Likely church for the Presbyterians was probably Dunboe 1syt Presbyterian whose baptism records go back to 1805 (with gaps). Marriage records start in 1845. For the Church of Ireland, Castlerock’s records start in 1870 & Dunboe St Paul’s in 1839. (Earlier records were burned in an explosion in Dublin in 1922). Copies of remaining records are in PRONI.
The land in Ballywoolen was held by the Worshipful Company of Clothworkers, one of the London Livery companies that originally settled Co Londonderry in 1610. I suspect the land was originally given to a single Duggan in the 1600s by the Clothworkers.
Some will abstracts (originals with PRONI in Belfast):
Full Abstract :
Dugan Matthew of Ballywoolen Castlerock county Londonderry farmer died 29 December 1925 Administration Londonderry 1 August to Emma E. Dugan spinster. Effects £164 8s.
Full Abstract :
Dugan Robert of Ballywoolen Castlerock county Londonderry farmer died 19 May 1921 Administration Belfast 7 May to Elizabeth Dugan the widow. Effects £167 7s. 6d.