I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse and al most non-existant prior to 1800. Many early B/M/D events weren't recorded, or the records didn't survive.
For John O'Donnell B 1827 +/- 4 yrs, somewhere in Ireland, with a father named John and mother Mary Burke, I found 0 records. This includes Co. Kildare.
I got the same result looking for John's parent's marriage.