A couple of ideas on how to find their birthplaces:
Naturalization records. Ohio's "first papers" (declarations of intent) required the applicant to state their last residence before emigrating.
The Cuyahoga County Archives has petitions and index to naturalizations, alphabetically by name, 1818-1971 at: Cuyahoga County Archives 2905 Franklin Blvd. Cleveland, OH 44113
How about church records? The church at which Mary's services were held and presumably, at which she was a member, was: St Ignatius of Antioch Church 10205 Lorain Avenue Cleveland, OH 44111 Tel: 216-251-0300