I was never able to trace any sailing information.
He went by the name Patrick Byrn according to the early census records. He was the Tax Collector on the Assessment Roles for 1843-45. Ballycastle, County Antrim was where they were supposedly from and it is a port town so they could have sailed from there to Liverpool where many of those emigrating to Canada sailed from. Byrn (Byrne & O'Byrne) were popular names on ships lists I have found. Hope you have better luck
finding more information.