Has anyone obtained a copy/official transcription of those NSW Births in the surname JOYCE .... as the online index does not include a father's given name, it is unlikely to be noted on the births, and the index entries suggest to me that the person registering the births was unable to give details of the marriage of the parents of the baby (when and where they married).
If the father were to register the births, even if not formally married to the baby's mum, then he is the informant. So on a different section of the NSW BDM cert he would be asked to nominate his relationship to the baby. So if Charles Gentry was the father of these babies, and if he was willing to state this when registering the birth/s, then you can have confidence that Charles was most likely the father. In that pre WWI era, the word recorded on those birth registrations may well have been "illegitimate".
However, where the parents of a baby were co-habitating, and unable to formally marry due to some impediment, then there's quite a few birth registrations where the father was the one registering the birth, and so he was able to state his relationship to the baby. It is simply that the online index (and all the usual off line indexes from past years/decades) draw the info for the headings FAMILY name and FATHER's given name from the first several columns of the registration, and NOT from the informant section....
ADD, just a gentle reminder that the surname on the NSW BDM births index is NOT drawn from the original registration for the BABY's surname. There was NO column heading (ie so no question asked of the informant) provision for the baby's surname until late 1960s (and those indexes are on restricted access). The index is drawn from the MOTHER's THEN surname .... so if she was a married woman, and (as likely in that era) using her husband's surname, then that's how the index has obtained that surname.
But, just because a bride uses a surname that she believes is her Dad's surname, that does not mean that person was her father....
Sorry for the long-winded reply, but I am not a skilled wordsmith.
Cheers, JM.