Peldrum,
James’ birth is long before the start of statutory birth registration in Ireland (1864). For events before that you need to rely on Church records, where they exist. You also need to know the person’s denomination. I note that neither of James’ marriages in Scotland was RC. The chances are that, if born c 1828, he was Church of Ireland in Fermanagh. (There weren’t many Presbyterians in that area and so Church of Ireland seems more likely, at that period). The surname is fairly common in Fermanagh with 415 in the 1901 census of the county. Mostly Church of Ireland.
Devenish Church of Ireland has records from 1706 but there are gaps. They go from 1800 to 1823 and then 1828 onwards. So if James year of birth is accurate, you may just scrape in. However he may have been a little older or younger than he claimed. People didn't celebrate birthdays in Ireland then and often didn't know exactly when they were born. Errors in ages are common. Plus the Devenish records may contain siblings and possibly his parents marriage. (There’s a gap in the marriages from 1825 to 1828). The records also contain burials, so they would be worth checking for James parents deaths.
I don’t think the Devenish records records are on-line anywhere. However there is a copy in PRONI (the public record office) in Belfast. A personal visit is required to view them or you could get a researcher to search them for you. Researchers in the PRONI area: http://sgni.net
I looked at Griffiths Valuation for Devenish in 1862. The only household with a George Thompson heading it then was in the townland of Fedian which is a rural agricultural area a couple of miles from Derrygonnelly. That George was a farmer with 20 acres. So not a clothier. So probably not your ancestor.
http://www.askaboutireland.ie/griffith-valuation/index.xml
Statutory death registration started in 1864. Derrygonnelly is in the Enniskillen civil registration area. I searched the records for a George Thompson who died 1864 – 1901. There were only 4 and none was of an age to be James’ father. So he may have died before 1864. There were 15 Mary Thompson deaths. One in 1866 for a woman aged 76, would be of the right age but most of the others were too old or too young. (There was one who died in 1865 aged 110, though obviously that may just have been a guess). If your James married 1855 onwards, the Scottish certificate should tell you whether his parents were alive or dead at that date. (It should say “dcd” if either was dead).