Cheryl,
How do you know David & Joseph were Church of Ireland? What records have you found to confirm that?
Church of Ireland graveyards were open to all denominations. Many other denominations often did not have their own graveyards eg Baptists, Methodists and some Presbyterians, so they often used the Church of Ireland for their burials instead. So being buried in a Church of Ireland graveyard does not necessarily mean that you were of that denomination.
David Alexander appears in the 1824 tithes for Lisnagunogue. In Griffiths c 1861, there’s 1 Alexander household out of about 10 farms. So in my opinion it’s fairly likely that it’s the same farm. Mathew Alexander appears t0 have been part of that family and in 1901 he’s down in the census as Presbyterian. So, if I am correct that it’s the same family, I suspect they were Presbyterian.
I don’t know if you are familiar with the 1803 agricultural census but it is on Bill McAfee’s website. David Alexander is listed in Lisnagunogue. His is the only Alexander household in the parish, though there are a few others in the general area. 18 households in the townland in 1803.
http://billmacafee.com/19centurydatabases.htm
PRONI has a document T1703/1 which is papers relating to the Antrim Estate (ie the Earl of Antrim). He was the main superior landlord for that part of Co Antrim. Page 59 in that collection, is a map of Lisnagunogue compiled in 1734. (Visit to PRONI required to view it, or pay PRONI to copy it).
Brian S Turner’s book: “Family Names in the Glens of Antrim” says this about the surname Alexander in that area (page 122): “Before leaving the Clan Allister some mention should be made of the modern surname Alexander, the non Gaelic form of Alasdair. The Alexanders of Menstrie, holders of the now extinct Earldom of Stirling are also said to be descended from the eponymous Alasdair Mor through his son Gilbert who got a grant of lands in Stirlingshire in 1330. The Alexander family who arrived in Ulster with the Plantation and were later granted the Earldom of Caledon in Tyrone claim to be related to the Menstrie family, although most Alexanders, like a large proportion of other lowland settlers, probably came from Ayrshire, or adjacent counties. The MacAlexanders of Ayrshire seem to be descended from Godfrey, second son of Alasdair Mor. They dropped the Mac at the end of the seventeenth century and the MacAlexanders who appear in seventeenth century Antrim are probably of this origin.” So Turner appears to be suggesting your Alexander family probably originated in either Arran or Ayrshire, or nearby. They probably moved to Ireland in the late 1500s or early 1600s. (Arran to Dunseverick is probably about 20 miles. No big distance).
One of my colleagues has kindly reminded me that there are some Church of Ireland records for Dunseverick. The parishes of Billy and Ballintoy had their boundaries re-drawn in the 1820s and a new parish of Dunseverick was created from land removed from Billy & Ballintoy. Dunseverick didn’t lose any records in the 1922 fire because they were stored safely in the church, and it has baptism, marriages & burials from 1832 onwards. (Copy in PRONI). Might be worth investigating for events after 1832, if the family are found to be COI. But unfortunately it’s not going to help with events in the 1700s. Whatever denomination the family was (and I think they were Presbyterian) no records exist for the 1700s in that general area.
One set of records you might want to look at is the Registry of Deeds. If the Alexanders had signed leases for their land, they may have been registered with the Registry of Deeds. Sometimes you get lucky, especially in the 1700s, and find a 3 lives lease which gives some personal information about the family. Not all leases, mortgages etc were registered, but many were. They can be found on the Familysearch site. They start around 1708 and run through to the 1930s. Search by townland name. (You can also search by surname but the index doesn’t tell you where the person lives so, townland is better.).