Hi ...
I checked FreeBMD for any Amy GREENs registered in Northamptonshire (being fairly local I know how the county boundary moves around in that area!) - nothing!
Then checked for Amy GREENs countrywide - still nothing in that timeframe.
Then checked for all GREENs (any forename) registered in Oxfordshire 1901-1903, and found this one:
Mar 1902
GREEN Female
Banbury
3a 1023
If you're reasonably certain of birth year/place, it could be worth ordering this certificate (although unless you have a good idea of parents names it may not help!). (Please recheck reference on FreeBMD website before ordering - I'm not infallible!)
Interestingly, there are no GREEN families residing in Banbury on the 1901 census, although plenty in the surrounding villages.
Hope this may help.
Pennie