ScotlandsPeople shows on 20/09/1774 a William Graham son of John Graham and Elizabeth McEuan at Stirling as the most likely candidate for his birth.
William Graham has a marriage to Kathrine Kinross on 19 Oct 1794 at Dunblane, Perth, Scotland
Daughter Margaret Graham born 1801 from census data. There is actually a birth recorded the christening of Margaret Graham on 29 SEP 1799 Saint Ninians, Stirling to this couple. However there was a further birth on 01/01/1805 of a Margaret Graham to William Graham and Catherine Kinross at St Ninians, Stirling. Her death certificate confirms that she is the daughter of William Graham and Catherine Kinross. Starting with her marriage, she keeps her date of birth at around 1800 for the rest of her life. In other words she was really 17 when she married but pretended to be 21.
The only other birth recorded to William Graham and Catherine Kinross is 09/02/1808 Thomas Graham at St Ninians Stirling.