Joe,
The Graham/Fleming tree on Ancestry has John McAtee(r) and Mary Keenan having a son Edward in Calton, Glasgow on 21.5.1873. There is a birth certificate that fits which says the parents married in Co. Monaghan on 15thAugust 1856. John was a carter and the informant was Mary who signed with her mark. They lived at 29 Brickfield Open, Glasgow.
Another child, Ann McAtee, was born on 4th May 1871 at 335 Gallowgate, Glasgow. That birth certificate records the parents married in Glasslough in Co Monaghan. That’s in the RC parish of Donagh. So we have a date and place for the parents marriage.
The RC marriage records for Donagh are on-line on the nli website. However the records are fairly hard to follow. I have looked for the 1856 marriage but could not see it. You might have more patience and be more successful:
https://registers.nli.ie/registers/vtls000632846#page/48/mode/1up
I searched for deaths for Owen & Catherine McAtee(r) in the Monaghan area 1864 – 1901 but there were none. So either they died before 1864 or had moved away from the area. (Did they move to Scotland too?)