My baby (15mths) has 8 nos. of teeth & 7 nos. have black stains, just like your baby. I have brought her to see my family doctor who replied that it is "teeth"-"qun"-"mok". There is no any harm for baby, just is the look.
The reason is some sweet food always stays on teeth. The most causes are (1) always put 'milk-(chase)' in the mouth. & (2) use a long time to drink milk.
My baby has no two above condition. When she is 14mths, she always eats e-tang-ka chees cake. She hasn't drink water immediately after eating. So, after abt 2-3 week, her all teeth suddenly change to black colour.
My doctor has give some "First-Teeth" teeth paste to me for brushing her teeth. It is safe to use because there is no any 'fut', so it can all to be eaten. You can also buy in Wing On dept store.
My classmate is a dential nurse. She stated that there are some baby have these black stains. It is no problem or any harm for the baby. When the baby can sit clam, you can bring her/him to clean teeth.
The above is my experience. When my baby smiles with no eyes & shows all black teeth. It is quite terrible!