would you have any idea as to why they would have put old/new on the birth entry (it was in 1826) in the OPR.
I don't know the area around Kilsyth at all well, but in Scotland the word 'town' or 'toun' didn't always mean a town in the modern sense. It could just mean a farm. Were there perhaps farms in the parish named Oldtown or Auldton and Newtown?
Also 1826 is just at the tail end of the time when it was fashionable for landowners to create new towns (in the modern sense) and villages. These are easy to spot because they always have straight wide streets in a rectangular plan, with the front elevations of the houses along the street. Older towns tend to have a main street that widens in the middle and then narrows again, with the houses on lanes to either side so the gable ends face the main street; they also have twisty wynds and lanes. Is it possible that the town of Kilsyth had been extended by the landowner some time in the early 19th century, and that the population referred to the original village as the 'old town' and the extension as the 'new town'?
I had a look at the 1859 Ordnance Survey Map, and it does look as if there are two parts to it, one with the classic straight streets of a planned village, the rest with the slightly random layout typical of older villages. Unfortunately so much of the town seems to have been obliterated and redeveloped that is it hard to see from the modern map whether any of it has survived.