Mary Green, born, 5th Aug 1867, Carrick-on-Suir, to Michael Green & Bridget Harnington.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1867/03472/2275340.pdf
Catherine's birth reg'd M quarter, 1872, MMN Hartnett.
There is also a record, not indexed, of Mary Green born to Michael Green and Bridget Harney, 1867, in Waterford. Harney could be Hartnett, but it's also a proper surname. On the 1871 census, her place of birth is Swansea but on every other census and document it is Ireland or Waterford.
Michael Jr is always listed as born in Swansea, and on his police record he is listed as born at St Josephs in Swansea. I'm not sure what is going on with the births. In any case, I haven't been able to find a record of Michael Jr's birth.
Long ... Kinda off topic but since it came up
I originally believed the wife was Bridget Harrington because of the birth record for Mary and some other circumstantial evidence. But, in 1881, Michael Jr is living with his aunt and uncle Lynch and I was never able to connect them to Harrington or Green. When the unindexed birth record for Mary was found, I realized that Harney and Hartnett were similar and researched that name. The aunt Mary Lynch was originally Mary Hartnett, Bridget's sister, so I am now confident Bridget was a Hartnett.
- I have never found a DNA connection to Catherine so maybe she is a half relationship, or no relationship.
- I have never found a DNA connection to the Lynch family.
- I have never found a DNA connection to any Green prior to Michael Sr.
The lack of a DNA connection doesn't prove anything.
Speculation ... I have no evidence for any of these.
1) Michael was married twice, Harrington and Hartnett, but I doubt it because there is no record of either marriage.
2) Michael Green was an alias, and he was running from trouble.
3) Catherine is not Michael's child.
4) Michael ran away from his family and changed his name. Possibly going to America.
5) Michael moved to find better work, prepare a new place, and something happened to him.
6) Michael got waylaid, thrown into the river and disappeared. Or got drunk, fell into the river and drowned, and washed away.
7) Michael died in the copperworks and it wasn't reported.
Mary Lynch nee Hartnett
https://www.familysearch.org/tree/person/details/GF9L-518