1. Do you have any dates of birth, marriage, death for your ancestor John Finlay and wife Mary Ann? They at least must have married before 1845 when your ancestor James was born, and still lived at Annyart c. 1855-1860.
2. How did you determine or learn their other children's names in addition to James?
3. What church did your Finlays attend in Ireland, if you know? Probably Church of Ireland or Presbyterian, and that's where they would have registered their children's births.
4. Did John & Mary Ann remain in Ireland, or did they or any of the other Finlay children besides James emigrate to America? (by which I'm assuming you mean the United States rather than Canada)