Conroy

Robyn,

Birth registration didn’t start in Ireland till 1864. Prior to that you need to rely on church baptism records. To do that we need to know what denomination John Conroy was.

In the Catholic tradition it was custom to baptise a child within a few days of birth, normally in the parish where the birth took place. If this family was Catholic then I have to say that in the 1830s being born in Belfast and baptised 50 miles away in Clonfeacle, would be most unusual. Not impossible but rare.  What’s the evidence for the 2 events both relating to your ancestor? (The name is very common. In the 1901 census there were 358 people named John Conroy in Ireland).

Ideally we need parents names to be sure of finding the right birth. You might get that from a marriage or death certificate.

Most people in Ireland in the 1800s did not celebrate birthdays and often had little idea of when they were born. If officialdom later asked for an age or date of birth it was common just to guess or make one up. So the standard advice is to search 5 years either side of any given age or date.