I saw a video on YouTube of a vendor in China selling different color chicks. I didn't understand or agree but I believe the people that commented on the video said they add food color to egg at a certain time before hatching.
There are some chickens that naturally have green feathers. I had an EE once that had LOVELY green feathers mixed in with the black ones. He was so pretty. How about looking for a chicken that is already green? Dye is not only unhealthy for them but it wears off. Put wanted ads up and see if anyone response to them. Be patient. From what I've heard, Black Sex Linked chickens can have a green sheen on them too as well as many other breeds that are black such as Australorps.