I think the location that William Morgan came from was probably the parish of Donaghcloney (rather than Derrycloney). There’s nowhere called Derrycloney in Co Down. However Waringstown is in Donaghcloney parish.
If William’s father was a farmer in that area, he could be in the tithe applotment records. The records for that parish show just one Morgan. He was J. Morgan in Monree townland:
http://www.irishgenealogyhub.com/down/tithe-applotment-books/donaghcloney-parish.php
By the time of Griffiths Valuation (1864) there was a Robert Morgan there on plot 4 which was a 13 acre farm. (Suggesting J. Morgan was dead). That farm today would be on the modern Monree Rd, just east of Donaghcloney village. (A couple of miles east of Waringstown).
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameS…
I found a marriage for Robert Morgan of Monree to Anna Moles on 31.1.1862. Robert was 27 and his father was James Morgan. So that’s promising.
That family still there in 1901:
http://www.census.nationalarchives.ie/pages/1901/Down/Donacloney/Monree/1243433/
And in 1911:
http://www.census.nationalarchives.ie/pages/1911/Down/Donacloney/Monree/252290/
Probate abstracts:
Probate of the Will of Robert Morgan late of Monree County Down Farmer who died 21 October 1914 granted at Belfast to Thomas Cluff and Robert Watson Farmers
Morgan Robert of Monree Donacloney county Down farmer died 28 December 1947 Probate Belfast 15 April to Maurice McAteer farmer and Alexander Campbell contractor. Effects £343 18s.
The family was Church of Ireland. If you are looking to confirm your William born c 1832 came from this same family, you would need to check Donaghcloney Church of Ireland records. They start in 1697. There’s a copy in PRONI (the public record office) in Belfast. Baptisms, 1697-1927; marriages, 1697-1994; burials, 1697-1919;
