cmn9534
Ginn is not a very common name in Fermanagh. Looking at the 1901 census there were only a handful of families and most of them lived near Irvinestown, in the parishes of Drumkeeran and Derryvullan. All would have been Church of Ireland in the early 1800s. You could try searching church records in those parishes.
Derryvullan’s early records start in 1803 and are on-line on the IGP site. I searched them but did not see any James Ginn marriage or children to him. Drumkeeran’s records start in 1801. They don’t appear to be on-line anywhere. However there is a copy in PRONI (the public record office) in Belfast.
Several Ginns farming in Derryvullan in the 1835 tithe applotment records;
https://www.irishgenealogyhub.com/fermanagh/tithe-applotment-books/parish-of-derryvullan.php
Tradition was to marry in the bride’s church, after which she’d usually attend her husband’s.
You say that Mary Guthrie cam from Dromore Co Down. That’s possible but it’s about 100 miles from Fermanagh. How would they have met? There is another Dromore in Co Tyrone and it borders Derryvullan parish. That seems a more likely origin for her. If the Guthrie family was Church of Ireland then the bad news is that Dromore’s records were all destroyed in the 1922 fire in Dublin. If she was Presbyterian (a distinct possibility, given a Scottish surname like Guthrie) then unfortunately Dromore Presbyterian has no records earlier than 1835. So it’s possible the couple married in Dromore, Co Tyrone and that there are now simply no records to find.
If it is any consolation, marriage records from the early 1800s contain very little information. Normally just the date, the couples 2 names and their 2 witnesses. No parents names etc.