Searching McGonigal, Matthews, Murphy, Harrington, Quirk, Smith, Bowen

You say William McGonigle married in 1856 in Ballyshannon but you don’t mention his bride. I assume it’s Jane Maxwell from Pettigo.  According to his marriage certificate, William was living in Bundoran, Co Donegal, at the time and his occupation was a scripture reader. His father was Bernard McGonigle, a farmer. (It looks superficially like Edward on the marriage certificate but I am pretty sure it’s Bernard).

https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1856/09503/5444187.pdf

You say that William was born in Ballymoney, Co Antrim c 1835. That seems slightly unlikely to me. McGonigal is not a surname common in the Ballymoney area. Indeed there isn’t a single one in the parish in the 1817 census. On the other hand it is very common in Co Donegal where William was living in 1856, and I’d have thought that’s a more likely county of origin.  There is another Ballymoney in the parish of Burt, Co Donegal. I suspect that’s a more likely place of origin.

Griffiths Valuation for 1858 lists a John McGonigle living in Ballymoney, Burt. He had plot 5c which was a labourer’s cottage. Perhaps a relation?

https://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch

You speculate that William’s mother was Elizabeth Holland. That’s a surname that is found around Ballyshannon. My thinking therefore is that the family is more likely to have Donegal roots rather than Co Antrim.

If you are looking for William’s baptism we need to know what denomination he was. I note that when he married it was in the Church of Ireland (ie Anglican) in Inishmacsaint church. Tradition was to marry in the bride’s church  so that only tells us she was likely Church of Ireland. William might have been RC (though the occupation of scripture reader makes me wonder about that). Anyway if he came from around Bundoran then the parish is Inishmacsaint. The RC church there has no records before 1847. The Church of Ireland has 3 churches in the parish (Inishmacsaint, Slavin & Finner) Slavin’s records don’t start till 1836 but Finner has records from 1815 and Inishmacsaint 1813. If the family comes from the parish of Burt, then the Church of Ireland records start in 1829, RC in 1859. Copies of all sets of records are held in PRONI (the public record office) in Belfast.