Hi James,
It is fantastic that you are researching your Griffith ancestors! It is also very helpful that you already know where they came from.
Before 1864 records were kept in the form of church and parish records; while some of these have regrettably been lost over the years, all the surviving records have been sorted into county-based
genealogical centres. In your case, the genealogical centre would be the
Cavan Genealogy Centre.
Because you know the place they were born at, you can also search the
Church records on the Irish Genealogy website.
Have you been in touch with the Cavan Genealogy Centre yet?
I hope this is helpful, please let us know how the search goes.