John,
The death record snip isn’t attached to your post.
However, knowing that Patrick was a farmer is helpful. Farmers should normally have been listed in the tithe applotment records (which were a tax on land). I checked the tithes for Co Down and there is only 1 Patk Mason listed there in 1833. He lived in Ballyplunt which is a townland in the civil parish of Rathmullan (RC parish of Bright). See:
http://www.irishgenealogyhub.com/down/tithe-applotment-books/rathmullan-parish.php
Death registration only started in Ireland in 1864, so clearly we won’t find a death certificate for your Patrick if he was dead by 1859. I searched for a death for Catherine. There were just 6 in Co. Down. All were in Downpatrick registration district, which includes Ballyplunt, but none was old enough to be your family. I suspect therefore that Catherine died between 1859 and 1863.
There’s a Catherine Mason from Bright parish who was noted as a sponsor of an RC baptism in 1861:
http://freepages.rootsweb.com/~rosdavies/genealogy/SURNAMES/M/Mason.htm
As far as church records are concerned, the RC parish of Bright only has baptisms and marriages starting in 1856, so not nearly early enough to be able to find John Mason or his parents.
Ballyplunt is not big. In the 1901 census there were 14 properties and a total population of 63.
There was a Margaret Mason living in Ballyplunt in 1859. She had a farm labourer’s cottage (plot 1b). She might be a relation to the Patrick who farmed there in 1833. Usually when a woman is listed in Griffiths, she’s a widow.
http://www.askaboutireland.ie/griffith-valuation/index.xml
Margaret Mason’s name remains as tenant in the Valuation Records until 1873 when she is replaced by Margaret Moffat, indicating she had moved or perhaps died. However the 1901 census lists a Margaret Mason in Ballyplunt. Not sure if it's the same Margaret. She’s aged 61 though ages need to be taken with a pinch of salt as they are mostly guesstimates. By her death a couple of years later she's 75.
http://www.census.nationalarchives.ie/pages/1901/Down/Tyrella/Ballyplunt/1229613/
She was married to Edward Mason. She had a son Patrick who married Elizabeth Hanna in 1895, when his address was Ballyplunt.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_re…
I looked for Edward’s death 1867 to 1901 but could not find it.
I found Patrick’s birth in Ballyplunt on 21.2.1867.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1867/03502/2287037.pdf
Patrick in 1901:
http://www.census.nationalarchives.ie/pages/1901/Down/Ormeau/Shamrock_Street/1213196/
His family in 1911:
http://www.census.nationalarchives.ie/pages/1911/Down/Tyrella/Ballyplunt/238911/
Mgt death:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1906/05574/4565322.pdf
Informant was Edward Rathmullan, Lower. This is him in 1901. I think Margaret was his mother and if so, her maiden name would have been Denvir.
http://www.census.nationalarchives.ie/pages/1901/Down/Tyrella/Rathmullan_Lower/1229637/
I would say there is likely to be some connection between the Patrick Mason & family in Ballyplunt in 1901 & 1911 and the Patrick Mason who lived there in 1833. Patrick Mason's name was still listed as tenant in 1929 when the Valuation Records stop.