I search Irishgenealogy.ie, a new, free, online database (among others).
For Denis Shanahan B 1829 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 6 rcds: 1827 Tipperary, 2-1828 Cork, 2-1830 Limerick, 1831 Limerick, and 1830 Kerry. Father's forenames were Patrick, John, Daniel, Daniel, James, and Jeremiah.
For Mary Carr B 1831 ditto, I found 47 rcds - too many to easily summarize here.
It would help if you knew their DOM/POM; it's easier to find an M rcd than isolated B rcds.