Here’s a transcript of the headstone in Kilbride Graveyard:
In memory of JAMES BRYSON, Holestone, who died 27th March 1878 aged 75 years. His wife MARTHA ANN who died 9th [Aug] 1870 aged 59 years. Also their children, LIZZIE died 28th March, 1858 aged 10 years. THOMAS died 27th Aug 1860 aged 19 years. JAMES died [in] Australia 23rd May 1861 aged 27 years. JOHN died 5th March 1864 aged 26 years. ROBERT died 13th May 1872 aged 21 years.
There’s nothing there to indicate that James Bryson (c1834-1861) was not the son of James Bryson (c1803-1878) of Holestone.
Here’s the marriage record from Donegore 1st Presbyterian:
July 5 1831. James Brison, Holestone, to Martha Anne McConnell Ballywee. Witnesses Jas Gawn Donegore & Thos McConnell Ballywee.
Unless there’s another marriage record of Martha Ann Bryson/McConnell to another James Bryson between 1831 and 1838, then I can see no reason to believe that James Bryson (c1803-1878) of Holestone is not the same James Bryson of Holestone who married her in 1831.
You mention that James Bryson travelled alone to Australia. It is not impossible that he left a wife behind. But his employer specifically described him as a “single man” during the inquest over his death. So I don’t see any reason to think that he is the James Bryson who married Agnes Boyd née Bryson in 1855.
I know I’m probably beginning to sound obstinate, but I don’t mean to be! I’m just trying to wrap my head around these connections. As you say, there are too many James Brysons – I’m up to 33 on my tree now!