Death records on SP in Ayrshire are very limited, Tarbolton only has parish records 1783-1785 &
1829-1848.
There are no McWhinnie deaths. There are a few baptisms after 1778 but no James 1761 in Tarbolton
The only birth and death of a James in the county but probably not the one you are seeking.
MCWHINNIE JAMES JAMES MCWHINNIE/AGNES DOWNIE Baptised 18/10/1761 Ayr
MCWHINNIE JAMES Died 19/08/1832 Ayr
One tree on Ancestry records James mother as Agnes Downie but that might be because of the lack of any other records.
Colin