Baby farmer : One who keeps a baby farm.

Example:


Taxonomy
Baby-farming, baby farmer, baby farmers, baby, infant, adoption, free encyclopedia, nurse, farming, baby farm, Articles lacking sources, Australia, hanged, Amelia Dyer, Amelia Sach and Annie Walters, assisted conception, British Medical Journal, lump-sum payments.

Defination from the web:
baby farmer in George Moore's Esther Waters (1894). The main character in Perfume, Jean-Baptiste Grenouille, was orphaned at birth and brought up by baby farmers. ...