Cornelius O'Connor, born in 1847
Mary O'Connor, born in 1860 (possibly died in infancy)
Joanna O'Connor, born in 1865 (possibly died in infancy)
Now, we look at the 1870 U.S. Census, which shows the O'Connor family (incorrectly transcribed as the Connin family) living in Yonkers:
Father: Daniel, born in 1825, employed as a laborer
Mother: Annie, born in 1822, works at home
Son: Jerry, born in 1852, employed as an apprentice to a machinist
Daughter: Norah, born in 1854, works at home
Son: Michael, born in 1858, works in silk shop
Daughter: Ellen, born in 1862, and at school
Son: John, born in 1865 and at school
Now fast forward 10 years and in the 1880 census, the family is still shown in Yonkers, living at 16 Irving Place. In the same building lives their newly-married daughter and her husband, Mr. and Mrs. Thomas (Nora) Ball. John and Ellen are shown as working in the carpet factory (most likely Alexander Smith & Sons), while Michael and Daniel are shown as laborers and Annie is keeping house. Jeremiah is shown living with his wife Ellen and children Charles, Mary and John on Park Hill Avenue.
Now, this is where the trail ends for Jeremiah, Michael and Ellen. Ellen most likely got married, but I haven't found anything yet which gives me a lead on her possible husband. Jeremiah seems to have left Yonkers, as did Michael, as neither of them appear in city directories in 1890 or in the census in 1900.
The research never ends!