Bill,
Scotlandspeople has a Church of Scotland marriage for Thomas Dowie to Sarah Dowie on 6.11.1829 in Sorn, Ayrshire. That’s a pay to view site. You need to register, and buy a few credits. It costs about £1.60 to view.
https://www.scotlandspeople.gov.uk
The 1841 Scottish census has a family that could possibly be that Thomas and Sarah. There’s a family of 13 people in Barony, Lanarkshire GROS ref 622/126/5. Head is Thomas aged 54 (so born c 1787) and wife Sarah aged 50, plus 11 others. You would need to view the census to decide whether it could be your family. (Again that’s on Scotlandspeople). Likewise they are in the 1851 census for Barony. 622/186/13. I don’t see Thomas or Sarah in the 1861 census. Presumably they had died or left Scotland.
Tracing the family back in Armagh could be difficult if you do not know where in the county they came from. The family appear to have been Presbyterian. Not many Presbyterian churches in Armagh have records for the 1700s. Armagh 1st Presbyterian has records for 1707-28 and then 1796 onwards but the records in between are lost. I am not aware of any others for the 1700s.