I think I may be of some help to you. Matthew and Mariah had a daughter, Sophia Anna O'Neil b. 1844. She married my 3rd great uncle, Thomas McCarty, Nov. 27, 1866 at St. Mary's church in Monroe, Michigan. She was also baptized there with her siblings.
Thomas and Sophia had the following children: 1. George McCarty, b. 1867 in Lulu Village, Ida Township, Monroe County, Michigan
2. Matthew John McCarty, b. Aug. 11, 1873 in Lulu Village, Ida Township, Monroe County, Michigan
3. Thomas A. McCarty, Sr., b. 1875 in Lulu Village, Monroe County, Michigan
4. Ethel M. McCarty, b. 1879 in Lulu Village, Monroe County, Michigan.
I hope this will be of some help to you. Should you later find anything else on the McCarty family please let me know. I am still trying to find more on the children and on Sophia. Thomas died dec. 20, 1895 and the farm was sold in Lulu Village. I don't know where Sophia and the children moved to after he passed away.