Just in case you do not have this census 1851. Kirkoswald, Ayr. Thats where your William Murray was born.
Address. Gate House.
Murray Alexander, Head M. M. age 28 years, Rabbit Cather, born Dundonald, Ayr,
Murray Sarah, Wife, M. F. age 23 years, Domestic Duties, born, Dalry, Ayr,
Murray Isabella, Daur, U. F. age 2 years, born Dalry, Ayr,
Murray William, Son, U. M. age 11 months, born Kirkoswald, Ayr,
Campbell Magdaline, Nurse, U. F. age 11 years Childnurse, born Dalry, Ayr.
By the way the Magdaline Campbell, age 11 years childnurse, is the younger sister of Sarah Campbell, Alexanders, wife.
Did William Murray, die in Bootle, England, ie Liverpool.