Why would a crown appear more grey after about 6 months?

There is a good chance there may be leakage under the crown.  This will cause the tooth to turn slightly gray.  I would schedule an appointment with your dentist to have it examined.  Good luck.  

There are two things that will make a crown grey after a short period of time. The first is micro-leakage. This is due to an open space ate the margin of the crown and bacteria are leaking under the crown causing it to become dark. This usually starts where the crown meets the gum. The second is if the tooth under the crown becomes very dark. This is an indication the tooth has died. Your daughter may possibly need a root canal. If the crown is thin this darkening may show through the crown. I suggest meeting with your dentist to discuss your options.