For James Colgan B 1889 +/- 4 yrs, Co. Armagh, with the father's forename unknown, I found 1 rcd, 1891, Loughall CP. Father's forename is William. This doesn't match your data very well, but is the only such rcd within the relevant range.
For Ann Downey M 1892 +/- 4 yrs, Co. Armagh, I found NO rcds. B/M/D registration was civil after 1863. You MIGHT find her marriage record at the Public Records Office for Northern Ireland (Google PRONI).
For Ann Downey B 1860 +/- 5 yrs, Meigh CP, Co. Armagh, with the father's forename unknown, I found 1 rcd, 1864. However, the father's forename is John.
For William Downey B 1855 +/- 5 yrs, Co. Armagh, with a father forenamed John, I found 1 rcd, 1856, Co. Tyrone (which abuts Co. Armagh), for a William John. The parish is Clonfeacle RC.
For James Colligan B 1867 +/- 5 yrs, Co. Armagh, with the father's forename unknown, I found 3 rcds. Details,father's forenames, and RC parishes are:
Baptism Colleghan James 1865 Co. Armagh, Peter, Armagh RC Baptism Colgan James 1861 Co. Tyrone, Francis, Clonfeacle Baptism Colligan James 1863 Co. Armagh, Michael, Upr Kileavey
These results are all tenuous since they don't match your criteria precisely. Hope this helps. Good luck.