I search the IFHF database at rootsireland.ie. It has 19 million B/M/D records. The database is about 90% complete.
For a Martin Ryan married 1850 +/- 5 yrs somewhere in Ireland to a bride named Catherine, I found 6 records with ONE in 1854 exact. The County is Limerick.
These MAY or MAYN'T be for your ancestors, but the possibility should be further evaluated with whatever other info that you have. Suggest you try to search immigration records starting with Ellis Island. Ellis may not have it there, but can give you insight into where other records are located.
Will leave it to you to visit the database and search for Martin's B record in/about 1812. Note B/M records from this era are very sparse.