Looking at all the later records they appear to have been RC.
The problem with that is that, as Aghadowey has told you, Mountrath baptisms only go back to 1823, too late for Denis but you may have luck getting Anthony's record.
These will be online, for free, from July 8th through the NLI, not searchable by an index, you will need to trawl through one page image at a time, but you might get a lead.
rootsireland is a sub site which has these records already, searchable, but again, a paid sub site.
There is a very short window of burial records for Mountrath, 1882 - 1899.
Fento, Denis' father I would imagine was long deceased by then.
Another avenue is to go to irishnewspaper archives, another paid sub site, but you could trawl though to see if there were any death notices etc ~ the Leinster Express has recently gone onto the site.
Tara
