Canisp,
There is a gravestone in the old Cambusnethan churchyard with the simple inscription -
"1843 Erected by John Moffat and Janet Thomson in memory of their children".
There are records for this plot but they only begin near the end of the 19th century. Here's what there is.
Owners listed as John Moffat and Janet Thomson.
(As always, dates are of internments)
In the South lair -
JAMES MOFFAT, aged 63 years. 5th April 1909.
In the Centre lair -
JOHN MOFFAT, aged 68 years, 28th April 1888.
In the North lair -
MARGARET MOFFAT, aged 86 years. 26th March 1906.
There is a corresponding entry in the Day Book for James.
JAMES MOFFAT, railway porter, Airdrie, aged 63 years, married.
Parents - John Moffat and Margaret Twaddle.
Interred in old churchyard 5th April 1909.
There is an entry in the paupers burial book -
JOHN MOFFAT, coalminer, Palacecraig, aged 14 years.
Parents - John Moffat and Margaret Twaddle.
Interred in old churchyard 28th January 1867.
I found a lair in the new cemetery, section D number 436.
All of the following are buried in it.
JAMES MOFFAT, engine keeper, Wishaw, aged 56 years, married.
Parents - John Moffat and Janet Thomson.
24th May 1892.
JOHN MUIR, miner, Wishaw, aged 20 years, single.
Parents - John Muir and Agnes Thomson.
18th June 1896.
AGNES F.F. MUIR, Wishaw, aged 2 years.
Parents - Charles Muir and Jane Moffat.
18th June 1896. (same day as last burial).
HENRY FINLAY MUIR, ironworker, died Glasgow Royal Infirmary, usual residence 21 McAlpine St Wishaw, aged 24 years, single.
Parents - John Muir and Agnes Thomson.
14th November 1908.
AGNES MUIR, Wishaw, aged 58 years, widow.
Parents - William Thomson and Marion Finlay.
26th March 1912.
Hope this leads somewhere. Palacecraig is just outside of Airdrie.
Lodger.