Hi Avril,
This information comes from the Carnwath old parochial records at Register House Edinburgh. I transcribed the Carnwath burials some years ago, the list of burials is on book 3 of the microfilm records - 632/3. The list begins at 1826 and ends 1854.
There are some mortcloth records in 632/2 from 1716 - 1729. There are no deaths (or marriages) recorded between 1729 and 1825.
Here are the other Alexanders in the Carnwath book.
All have the surname Alexander - dates are presumed to be of burial.
Infant - 28th Feb 1832, Forth. 4 months.
Robert - 14th April 1837, Forth, 2 years.
Jean - 11 Jan 1839, Forth, died of a cold, 2 years.
Thomas - 24th July 1840, Carnwath, 20 years.
William - 26th DEc 1840, Forth, fever, 3 years.
James - 5th April 1842, Forth, old age, 82 years.
John - 1st June 1849, accident, aged 12 years.
Agnes - 2nd June 1853, died in childbed, 19 years.
John - 23rd Feb 1854, Carnwath, cancer, 49 years.
William - 30th March 1854, Forth, decline, 11 years.
Hope that helps a little,
Lodger.
Infant,