You give no location for this family - only that the father was born in Canada and the mother was born about 1855 in Ireland. But you posted in the California forum; did they live at some point in California?
Is this your family in 1880? From your list of kids they would have had only Mary M. (born ca 1879) at that time.
1880 Fremont, Santa Clara, California M. Oconnor 35 born about 1845 in Canada, farmer Mary Oconnor 22 born about 1858 in Ireland Mary M. Oconnor7 months, born in California
As you say, finding a couple of "Mary Oconnors" is not real compelling evidence, as this is a common name. The more detail you can provide, the more you set up your volunteer researchers for success.
Just showing you how many people like her are floating around out there; at least a couple have parents Matthew and Mary.
I usually recommend a person spend about an hour or two hours on a query in a case like this - where you are a seasoned enough researcher (and I think you are) that you probably have quite a bit of information to organize and share.
I think you'll get a good response if you follow my advice; I was given the same advice when I started and it did the trick!