OK, at irishgenealogy, now have what appears to be your John James recorded as McInly, born what looks to be first Nov 1876 at Cross Street (so still same general area), to father John, Militia Man.
The mother is what looks to read Margaret, albeit shown as formerly Long. That said, neither parent registered the birth, so there is obviously the possibility that Margaret's surname could be incorrect (the woman who registered the birth signed with 'her mark', so wouldn't necessarily have noticed if there was a mistake or she may have said Long in error).
Same entry indexed at
https://familysearch.org/ark:/61903/1:1:FGK9-8S9 Whilst there are Margaret/Maggie Long marriages in the are around the timescale, none so far seem to be to John.