This is what the indexes to the original records show.
John Baird and Helen Watson were married in Glasgow in 1817. Their family were
Archibald, baptised 1818 in Mauchline
Jean, baptised 1820 in Leith
John, baptised 1822 in Leith
William, baptised 1824 in Greenock
In 1841 the family, minus Archibald, were living in Meadowbank, Edinburgh.
Have you viewed all the baptism records? Are the witnesses' names recorded, and if so do they provide any clues?
Archibald Baird and Agnes Bell had eleven of a family, five baptised in New Cumnock then six baptised in Mauchline. If I were you, I would be looking at some of those baptisms to see if they resided in the same place where John B and Helen Watson were when their Archibald was baptised.