Ann,
Regarding searching for gravestones, you could certainly try the Ulster Historical Foundation website but I don’t know if they have any records for the graveyards I have mentioned.
http://www.ancestryireland.com
The graveyards may not be attached to any church, or if they are, I don’t know which that would be. Derrynoose Old graveyard, I am sure will not be attached to any church. Unless someone has transcribed the gravestones and put them on one of the pay to view sites, often the only way to find a gravestone is to go in person (or pay a a researcher to do it for you).
There are very unlikely to be burial records for someone buried in the 1880s and so if there’s no legible gravestone, then locating the grave may prove pretty difficult.
If Bernard was a farmer, then that increases the chances of there being a gravestone. The vast majority of the population couldn’t afford a gravestone and were buried in unmarked graves. However your chances with a farmer are a bit better, as they were usually a bit better off than the average labourer. Occasionally a relative overseas paid for a gravestone, so that can be a possibility too. (You will frequently see stones with inscriptions saying things like “Erected by son William in Ohio” etc).