Here are possibles from ScotlandsPeople from 1855 - 1861, for all districts
1859 Dunlop Janet Coylton AYR
1859 Dunlop Janet YOUNG Riccarton AYR
1859 Dunlop Janet Anderson Stewarton AYR
1860 Dunlop Janet Fenwick AYR
Anderson is a christian name, whist Young is an other surname.
Jamjar