These “suburbs” appears to have been centered between Avenue M in today’s Midwood and Flatlands to the south.
Greenfield “was laid out in 1851 on 67 acres of land which the United Freeman’s Association had bought from Johnson Tredwell,” reports The Eagle and Brooklyn, from 1893.
“To this property they added the Ditmas farm in 1852, making a total acquisition of 114 acres.”
The Greenfield name didn’t last long; the town was renamed Parkville in 1870. Still, its main streets named after trees (like Elm, which starts across from the M Street subway station) that don’t conform to Midwood’s neat street grid remain.
South Greenfield appears to have hung on a little longer. It’s marked on this map from an 1895 New York Times article on Brooklyn suburbs. (Look in the center, off of “Smith Street Trolley.”)
“The pretty village of South Greenfield lies on the line between Flatlands and Gravesend,” another 1895 article says, cryptically alluding to its attractions.
At some point in the decades soon after, South Greenfield disappeared.