It's always tricky trying to find deaths before 1855.
If he was a pauper mason it's unlikely that the newspapers would have reported his death, but I have checked anyway and found nothing in the British Newspaper Archive.
It's unlikely that a pauper family would be able to afford a gravestone, but it may be that the family prospered later and eventually commemorated him on a gravestone. I do not know, however, if there are any online sources of gravestone incriptions in Dunoon and Kilmun. In 1997 the Scottish Genealogy Society published a booklet of Monumental Inscriptions in Kilmun churchyard, so maybe someone who has a copy of this would be willing to check for a record there of Alexander Grierson's death.
As for church records, Ardentinny is in the parish of Dunoon and Kilmun. The only extant pre-1855 burial records from this parish are from 1755-1772.
Sometimes the Kirk Session records include accounts, and such accounts record payments for the use of the mortcloth (a cloth used to cover the coffin during a funeral service) which may name the deceased person. The surviving Dunoon and Kilmun Kirk Session records are online at
www.scotlandspeople.go.uk. I took a quick look at some pages of the minutes, but did not see any record of mortcloth payments there. There are records of mortcloth payments in the Kirk session and Heritors' minutes (CH2/456/4) but the ones I saw did not name the deceased. You may like to make a more thorough search of these records in case I missed something.
There is one other possibility. A pauper, after 1845, is specifically someone who receives assistance from the Parochial Board, and parochial board records, if they have survived, are a very useful source of all sorts of information including the death of the pauper. I do not know whether or not the parochial board records of Dunoon and Kilmun have survived, and if so where they are, but I would start by asking Argyll and Bute Council Archives
https://liveargyll.co.uk/facility/archives/Failing all this, you'll just have to do like the rest of us and record his date of death as 1851/1854!