Information on marriage certificates is usually more reliable than death certificates which, by their nature can never be first hand. I’d assume Matthew’s father was probably Alexander.
If he’s from Co Derry then the 1831 census has survived. There was one Alexander Stevenson/Stephenson in it, in Knockbuck (more commonly Knockbrack) in the parish of Clondermot. 3 males and 4 females in the family, so probably a married man. Denomination was Presbyterian, whereas I notice that Matthew was buried in an RC service so that doesn’t fit terribly well unless he changed denomination.
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Carnan_Upper/Knockbuck/2/
There were very few RC Stephensons in Co Derry in 1831. The name was mostly Presbyterian.
Beard is not a common name in Co Derry. About 10 households in the 1831 census. Mostly Presbyterian or Protestant of one variety or another. No Beards in Clondermot (folk tended to marry locally in those days). So no obvious leads on Matthew’s place of birth.