excerpt from: ASTM-B633 ZINC plating;
http://www.techplate.com/zinc_cad.htm
Properties of the Chromate Finish
Even though zinc and cadmium are excellent rust retarders the surface of steel coated with these metals does not remain bright and stain-free in service. To avoid staining and delay the formation of white corrosion products during storage or in service indoors, practically all zinc and cadmium-coated steel manufactured today is given a thin (20 micrometres maximum) protective film using one of the available chromate conversion finishing processes. There are three classes of chromate finishes in general use on cadmium and zinc coatings: blue brite, clear (single dip or leached) iridescent yellow, black and olive drab. The thickness of the finish increases in the same order, the olive drab being relatively much thicker than the others. Which class of finish is selected depends upon the kind of service to be met and the properties desired in the finish.
I am not sure if you can post treat a black Zinc job with a additional chromate conversion coating to get the green tint. I could be possible.
Jim