Hello,
I found on
www.rootsireland.ie an index to the marriage for Francis Coyle and Elizabeth Hagan, which took place in Cookstown in 1899. I also found another child born to them who was Rachel Coyle b. 1899 in Cookstown. I can't find Thomas's birth in Co. Tyrone however but I can see now he was born in Scotland. However Rachael isn't on the census so I presume she died in Scotland before the 1901 census..I can't find her death in Ireland.
I see from the 1901 Census of Scotland, that both Francis and Elizabeth were born in Armagh, Ireland. From rootsireland.ie, I can see 2 matches for births for an Elizabeth (O) Hagan born around 1879 (she was 22 on 1901 census):
Elizabeth O' Hagan 1880 Lower Killeavy, Co. Armagh
Elizabeth Hagan 1881 Armagh, Co. Armagh
For Francis Coyle, I can only see one birth around 1878:
Francis John Coyle 1875 Armagh, Co. Armagh
Hope this helps,
Annie