Hi Isobel
Have you discounted the English birth entries showing on FreeBMD. For example:
Births Sep 1901   
Rogers    Elizabeth   S.Shields    10a   847
Births Dec 1901   
ROGERS    Elizabeth    S. Shields    10a   839
On Scotlands People, there are only two possible birth entries between 1901-4 in Hamilton:
1901   RODGER   ELIZABETH CROSS   F   HAMILTON   /LANARK   647/00 0388
1902   ROGERS   KATHLEEN ELIZAB   F   HAMILTON   /LANARK   647/00 1150
Was either of these the one you have already discounted?
Regards.
Monica  
