Hi
Your best bet would be trying a parish church in Wexford where your great grandfather & his father was living. As they will be able to look up in the parish register book to see if there are burial records on them. Sometimes the graveyard is near to the church--maybe a parish priest will send a volunteer to look around to see if they were buried with a headstone with dates or not.
Another suggestion is to keep your mind open about the surname's spelling variants--I know the GRO will only search on the surname you gave them--will not search other variants as they told me that they are NOT a genealogical service once.
You would have to look up in the GRO Indexes to see if your man is there. You have two options:
1) Go to the LDS/Family History Centre to view the GRO indexes yourself
2) Place a look-up request in the Death Indexes with this website
www.familyulster.com for only one pound per year and ask nicely if he/she would be kind enough to look up on variants of the surname's spelling especially in Co Wexford (we cannot be certain that he died in Co Wexford--he could have died anywhere in Ireland) since you have good name-- that will narrow the searches considerably.
They do have an access to the GRO indexes for the whole island of Ireland up to 1922.
Hope this help you in your quest for the information on your ancestors.
Kind regards,
Tees