Hi Robyn,
A good paper trail is essential when trying to trace family history and a Death certificate is perfect!
As he would have probably been born before 1864, the records would be held as church or parish records and all the surviving records have been sorted into county-based genealogical centres. The one for County Fermanagh would be
Irish World who have information for counties Fermanagh and Tyrone.
Indeed Ballymccaffrey is an old townland in Aghalurcher, County Fermanagh so the name is popular with the area. Bally, is derived from the Gaelic phrase 'Baile na', meaning 'place of', so this may be a great place to start looking.
Hopefully, there will be further suggestions from our other members, and please let us know how you progress.
Martin