There are two documents involved here, both of which appear related to Archie McIver's application for an Irish pension in 1920. Archie had emigrated to the U.S. around 1869, but later returned to Ireland (perhaps to apply for the pension). One document is a 1920 "Extract from Census Return of 1851), available at
https://www.ancestry.com/discoveryui-content/view/109933:70792?tid=&pid=&queryId=4369750c63845bcc419a96de3c25dce9&_phsrc=NWS18485&_phstart=successSource. One is the Church of Ireland form I sent yesterday, which is also available at
https://www.ancestry.com/discoveryui-content/view/2651:62061?tid=&pid=&queryId=748f0c283cc2e646a110b4d8d1daf45c&_phsrc=NWS18478&_phstart=successSource. The latter document appears to be drawn from parish records of the CofI church in Drumnakelly. Taken together, the documents outline a McIvor family in Bracky consisting of John (1811), Ann (1823), Jane (1832), Daniel (1836), Thomas (1841), Betta (Elizabeth?) (1843), John (1845), Archibald (1847), James (1851), Robert (1853), James again (1856), perhaps indicating the earlier James died in childhood, Hugh (1858) and Margaret (1861). Some of these ages from which the birth years are drawn appear on the 1851 census document, but the parish record add a bunch more, which I assume came from baptism records I have been unable to find anywhere else. Hugh, on a form filled out later in life, gave his mother's maiden name as Ann Cameron. The ages of some of the children weigh against Ann being their mother; there's a five-year break in the kids' ages which may indicate the death of a first wife after Daniel and Ann's arrival as a mother with Thomas. That is highly speculative.
My interest in this is John (1845), who I think was my great-grandfather. My grandfather was named Archie, which would make the Archie in this family unit his uncle. Several other names repeat in my grandfather's generation. Interestingly, both Archies wound up in the Philadelphia area.
At this point I am mainly looking for evidence DISPROVING my theory that this John McIvor is my great-grandfather. He doesn't appear in Ireland again, that I can find, so the main possibility that would exclude him for my purposes would be emigration.
If anyone knows of a way to access the Church of Ireland records in Drumnakelly, that would be helpful.