Just found out the names of Mary Ryan Walsh's parents. They were Thomas & Margaret Ryan.

According to the 1880 Bridgeport Connecticut census:

Margaret Ryan, 70, kept house, was born in Ireland as were her parents
Daniel Ryan, 40, son, blacksmith, born in Ireland
Martin Walsh, 36, son-in-law, laborer, born in Ireland
Mary (Ryan) Walsh, 35, daughter, keep saloon, born in Ireland
William Walsh, 9, grandson, at school, born in Connecticut
Edward Walsh, 7, grandson, at school, born in Connecticut
Maggie(?) Walsh, age ?, granddaughter, born in Connecticut