I searched the Irish Family History Foundation's online database for Co. Armagh. Rcds B4 1840 are sparse. Many events weren't rcd'd, other rcds were lost in time.
I found a "Patk" McParlan (+variants) B 1799. There is a slim chance this is your ancestor.
Assuming an M date for Pat of 1825 +/- 4 yrs, I found 2 matches: 1 in 1825, the other in 1826. You may want to try a range of 1828 +/- 4 yrs.
For the children: James B 1833 - 1 rcd in parish Ballymore, John B 1835 - 1 rcd parish Lwr Killeavy, Mary B 1839 - 1 rcd parish Killeavy, Catherine B 1841 - no rcd in Armagh, John B 1846 +/- 2 yrs - 4 rcds in Killeavy, Sarah B 1847 +/- 2 yrs - no rcds, Pat B 1848 +/- 1 yr - 2 rcds in Killeavy. It appears these are all in the same family. If so, viewing the B rcds SHOULD show the names of the parents.