Thanks for your trouble, Ralph - and please accept my apology for not replying for eight months.
I haven't yet dared to do any more Irish research. I paid one site for 'tokens' or 'points' to look at their records but came up with nothing, ran out of 'credits' and stopped. That particular site drives away business with that practice. They should be offering membership for a reasonable fee and unlimited record searches.
I've since learned a few things about Michael O'Mealy. He was married using that name in 1879. By 1881, when he and his wife had their first child, they'd changed it to Malley. Looking at the city marriage license, he states that:
1) He was from Limerick 2) His parents names were Michael and Ellen
I also now know that he had a brother named James who was a cooper by trade.
Nothing else is known.
When I get up the nerve (and the cash) again, I'll take a deep breath and jump into the deep end of the Irish records pool.
Thank you, Ralph, for the assistance you've given me. Things like that are both rare and hugely appreciated.