That index listing mentioned by Ruskie is a baptism. SP indexes 5 baptisms of children to Robert Sawers and Margaret Hay: unnamed child 1762 (tempting to think that this is his 'eldest brother' John, named in the newspaper article), Marion 1765, Robert 1768, James 1770, Peter 1773. Peter's death index says he was 86 when he died, which fits a baptism in 1773.
The 1851 census transcription lists at Nether Kirktonfield, Neilston a household headed by Peter Sawers, Deputy Lieutenant for the County of Linlithgow, Justice of the Peace, and bleacher employing 16 men, 33 women, 3 boys and 5 girls, born Dunbartonshire, Cumbernauld. It gives his age as 40, however, so I think if I were you I'd want to check the original to see if I agree that it is 40. The 1841 transcription says he was 45, which is also questionable.
As he owned land, the obvious source to look in is the Registers of Sasines. This is the record of changes of ownership of land in Scotland since the 16th or 17th century. They are mostly indexed, and they usually tell you the relationships of the people when there is a change of ownership. Neither the Registers nor the indexes are available online. You have to go to the National Records of Scotland in Edinburgh (or get someone to go on your behalf) to view them.
I see that in the 1851 census Peter Sawers, 42, born New Monkland, was listed as the Free Church minister at Gargunnock.
The Scotsman has many articles referring to Rev Peter Sawers. The earliest of these relate to litigation between him and his brother Henry over the execution of their uncle's estate. Later on, Rev Peter Sawers was convicted of defrauding the North British Railway by tampering with the date on a railway ticket, and this led to a long series of litigation and proceedings both in court and at the Free Kirk Presbytery, Synod and General Assembly. Unfortunately the images available online are very poor and I was able to decipher only about a third of them. I did not find an obituary.
He seems to be the Peter Russell Sawers, aged 70, who died in Edinburgh Newington in 1885.