Hello, we rely on parish records at that remove and not all parishes have records going back that far so any found may still miss your man as we do not know the father. However there is a Bryan Duffy born in 1809 in Haggardstown parish, address Dunbin (townland) mother is Mary Callan and father Mathew. There are other Bryan Duffy's born in Louth but not that close to the date, there is also two born in Armagh parish of Upper Creggan which borders Louth, the diocese of Armagh is made up of the counties of Armagh and Louth, nowadays Armagh is in Northern Ireland. One Armagh one is in 1815 others are later.
I found no marriage to a McEnaney in Ireland, searched up. to 1855. There are a number of Bryan Duffy marriages but not to the desired spouse.
There is a site here on Louth which may interest you
https://jbhall.clahs.ie/
DNA testing may assist in identifying the mother of Bryan.
The marriage of Bryan may have taken place in the brides parish so again not sure if records available but most had started by 1830.
Regards
Pat