I managed to find a few more burial records, all from Cambusnethan old churchyard.
First of all, a plot in the churchyard without a headstone in place.
The owner, in Victorian times, was Robert Douglas. 3 interments recorded.
AGNES TENNANT DOUGLAS, aged 63 years.
Interred 14th October 1924.
ROBERT DOUGLAS, aged 74 years.
Interred 14th February 1912.
JANE HAMILTON DOUGLAS, aged 79 years.
Interred 29th April 1918.
According to the Scotlandspeople index, the above Robert Douglas' mother's maiden surname was Young. In the Day Book register he is described as a portioner, Wishaw, son of Robert Douglas and Agnes Young. (A portioner owned a (usually) small piece of land, enough for a house and stable perhaps).
The above Agnes Tennant Douglas died in Milngavie (Mill-guy) and her mother's maiden surname was Dougal.
This plot is very close to the plot with the stone "Erected to Robert Douglas by his son James". (No. 111 in your records).
A few more entries I found in the Day Books.
This first one is, I think, one of yours but I'm not sure.
JOHN D. REID, Glasgow, (residence Liverpool) aged 5 years.
Parents - John Reid and Janet Douglas.
Interred 6th April 1874.
STILLBORN MALE LIGHTBODY, 6 Sneddon's Pit.
Parents - Thomas Lightbody and Christina Douglas.
Interred 30th August 1866.
THOMAS LIGHTBODY, Wishaw, aged 17 months.
Parents - Thomas Lightbody and Christina Douglas.
Interred 15th September 1871.
CHRISTINA DOUGLAS, Glasgow, aged 34 years, married.
Parents - John Douglas and Elizabeth Young.
Interred 31st December 1877.
THOMAS SOMMERVILLE, Wishaw, aged 2 years & 7 months.
Parents - Thomas Sommerville and Elizabeth Douglas.
Interred 6th March 1867.
ELIZABETH DOUGLAS, Wishaw, aged 67 years, widow.
Parents - James Young and Elizabeth Martin.
Interred 4th February 1873.
ELIZABETH HAMILTON, Wishaw, aged 46 years, married.
Parents - James Douglas and Janet Douglas.
Interred 9th June 1873.
If you can prove/confirm that the above Elizabeth Hamilton was married to William Hamilton and that he died early January 1899 then you can safely assume that the plot No.111 is the right one as William is recorded as being interred in that plot 9th January 1899 aged 74 years.
I will now go and search for any children of William and Elizabeth.