Familysearch.org does not seem to have the birth registration. If you do a Google search of West Cardiff, Wales genealogical you may find an appropriate resource
Here are the first 3 hits of 100or more:
In Wales, the county Glamorgan is occasionally referred to with the “shire” suffix. ...However, the county boroughs of Cardiff, Swansea and later Merthyr Tydfil had ... The county of West Glamorgan was divided into the newly created county ...
An index to births registered throughout England & Wales. ... Canton, St John, CardiffBaptism Registers (1907-1912) .... Western Mail Cardiff Directory (1911).
Genealogical research information about Glamorgan, Wales. ... Telephone: (029) 2087 2200 Email: GlamRO@cardiff.gov.uk · West Glamorgan Archive Service