Griffiths Valuation
There is one Patrick Goodwin listed in Tyrone in Griffiths Valuation.
Patrick Goodwin, Carnenny, Desertcreat, Tyrone
The time frame for Griffiths is 1848 to 1864 so it might well be that this Patrick is Mary's father. But you would need to contact the parish in that area to see if there is a birth record for her.