There were only 527 births registered in Ballina in 1907. If you want, it’s easy to check them all on the irishgenealogy site, looking for every possible permutation of the spelling, in case the birth is badly transcribed. I don’t see any that fits. So as Wexflyer suggested previously, it’s quite possible the family overlooked registering it.
It’s interesting that in 1914 they used the child’s baptismal certificate and not a birth certificate. Could that be because she didn’t have a birth certificate? What paperwork was provided for the other children? Birth certs or baptismal certs?
If you need the birth certificate because you intend to apply for something, it’s possible that the authorities will accept a baptismal certificate instead. I have heard of that being successful in some Irish citizenship applications.