Consistently green stools in the breastfed baby can indicate:
an imbalance of foremilk/hindmilk, often resulting in frothy green stools.
a sensitivity to something in the mother's diet, such as cow's milk products.
a sign that baby has an illness. Babies with an intestinal virus or even a simple cold will sometimes have green, mucusy stools. Teething can also bring about green stools due to increased saliva (can also cause tummy upset)
a lot of green vegetables or something with green food coloring in mom's diet.
If baby has started solids, that could also account for the change in color (this is normal with the change in diet).