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I have only just returned from a short trip to darkest Perthshire and, off the top of my head, the only church in the parish of New Monkland as far back as 1766 would have been the parish church at Greengairs. The village of Airdrie didn't have a church of its own until 1789 and, that was a Secessionist Church.
Here is an extract from an article I wrote for a local history magazine a couple of decades ago -

(East Monkland is the old name for New Monkland and, the chapel mentioned below is the "chapel of ease" which was built by the parish to "ease" the burden of the villagers who had to travel to Greengairs in the winter and in bad weather).

"It was obvious that Airdrie was in need of a church within the town, so why did the Heritors continue to ignore the needs of the villagers?  There was good local precedent for a chapel, Old Monkland had built one at Shettleston and another had been erected at Chryston in Cadder Parish.  Cambusnethan had one at Morningside, so it looks as though the Heritors of East Monkland didn’t want to spend any more than they had to.  I knew that a Secession church (a Burgher Church) had been established in the town in 1789, six months before the Chapel of Ease, and I suspected that this had been the catalyst.  A search of the Presbytery of Hamilton records (CH2/393/6/115) provided the evidence.  At a Presbytery meeting on 26th January 1791, a petition, address to the “Reverend Presbytery” was handed in, signed by 436 inhabitants of Airdrie & other Heritors of the Parish of East Monkland.  It went on to say   ….. has of late, prompted (by) the Dissentions of the Burgher association to attempt at getting a settlement in the village which will cause a division in the parish, which the subscribers wish to prevent, being all firmly attached to the Established Church.  The subscribers have long had it in their eye to get a Chapel of Ease erected ……… for the accommodation of the numerous old & infirm persons in the village who are unable to attend Divine Ordinances at East Monkland.  It goes on for quite a length and was beautifully worded; the Presbytery just couldn’t refuse".

So, Forfarian is correct.

I will go and have a look in the next couple of days, just to make sure it's still there. I have a little, hand-made plan of the churchyard and it's no trouble to check it out. I'll get back to you asap.

I also have an example in my tree where the number of children noted is less than those actually born to the couple, they appear to have just counted those still living at home.

Exactly as they were supposed to do. Anyone living at that address on the particular night that the census was taken, not anyone usually living in the house but absent on that night.

I've never come across this before. I can see on the screenshot that the mother had given birth to 9 live children and there seems to be 8 still alive. I can't imagine that, given the specific question about live children in this census, a mistake could have been made.
What is the mother's maiden surname?

Hi - thank you so much for the info, and apologies for my late reply. I can confirm that these are my ancestors. Can I ask where you obtained this information? I am in the states. Thanks again!

I have a copy of the Globe cemetery burial records, they were transcribed by a group of amateurs about 30 years ago, unfortunately, they didn't make a very good job of the work and I have found many mistakes over the years. The original books are with North Lanarkshire Archives at the Heritage Centre in Motherwell.