Hello Phamie,
Dont know if you have this, 1851, and 1861, census index, for Kirkmichael, and Girvan, the indexes are not the full census but are helpful in placing ancesestors.
1851, Kirkmichael, Ayrshire,
Coulter William, age 40y,
Coulter Mary, age 39y,
Coulter Elizabeth, age 19y,
Coulter William, age 14y,
Coulter Mary, age 9y,
Coulter John, age 1w,
Coulter Robert, age 1m.
You will find this families ages seem to be inconsistent with each census, and its a bit strange that John is 1w, and Robert, is 1m, could be a translation error.
1861, Girvan,
Coulter William, age 53y, born Ireland,
Coulter Mary, age 50y, born Girvan,
Coulter Elizabeth, age 29y, born Girvan,
Coulter John, Age 8y, born Girvan,
The only consistent age is Elizabeth, she is correct with your 1871, census, and she is the only Elizabeth Coulter, in Ayrshire, of that age.
Regards,
John.