I suspect he came to ireland via Scotland. I notice in the 1881 census that his oldest daughter Margaret was born in Scotland and found this in the 1861 Scotland census.
Name: Michael McShane Age: 42 Estimated Birth Year: abt 1819 Relationship: Head Spouse's name : Elizabeth Gender: Male Where born: Ireland Registration Number: 625/2 Registration district: Holytown Civil Parish: Bothwell County: Lanarkshire Address: Carnbroe Sq Occupation: Coalminer ED: 16 Household schedule number: 116 Line: 21 Roll: CSSCT1861_92 Household Members: Name Age
Elizabeth McShane 38 Elizabeth McShane 1 Mo Francis McShane 4 John McShane 12 Margaret McShane 14 Mary McShane 7 Michael McShane 42 Patrick McShane 6
The dates for the two daughters and his occupation tie in quite well. Noticed also that his daughter Mary was born in Ireland, which is puzzling. It could be an error.Do you know if his wife's name was Elizabeth?