Irish citizenship of 'illegitimate' son?

I'm enquiring on behalf of a UK citizen interested in possible Irish citizenship post-Brexit. He was born in the 1930s in the UK mainland to a non-Irish UK mother. His birth certificate records only the mother's name, although the identiity of his father, an Irish national, is known - supposedly paternity was established in local court proceedings at the time for the purposes of child maintenance. If this can be documented from court records, can he claim Irish citizenship, or does the lack of the father's name on the birth certificate make this a complete non-starter?

Does he have any legal document proving his father is an Irish national?

No, and I suspect this may fall down if the court records (assuming they can be found after all this time) do not provide sufficient additional information about the father to (e.g.) obtain a copy of his Irish birth certificate. But assuming it is possible to get hold of both the court records and proof of the father's nationality, would this be enough? The standard application process seems to require a named father on the son's birth certificate. Is this an absolute requirement, and is 'legitimacy' itself an issue?