I’m not related to any member of this family.
It's not likely that John and Ellen's parents are in the census records.
There are family trees on ancestry showing John's parents BUT there are NO sources for those names.
Michigan did not require “by law” birth, marriage & death registrations until 1867. So, there should be a death cert for Ellen. Death cert. usually shows cem. name + location and parents names.
Facts you should know about the early census records –
All census records [1790 – 1840] prior to the 1850 census ONLY listed the head of household; whether male or female.
NO specific age was stated for any family member
NO place of birth was stated – city, state, or country
NO city, town, or village is stated – only the county; however some census takers listed the township
NO street address was stated
NO marital status was stated – single, married, widowed, or divorced
NO family relationship was stated – brother, sister, cousin, son, daughter, wife, inlaw, etc…
NO occupation was stated
NO parental birthplaces are stated
NO race was stated [but assume “white”]
1850, 1860 & 1870 census records do not show family relationships, marital status or parental birthplaces.
Step children are not enumerated as “step” children
Adopted children are not enumerated as “adopted”
Grand children are not enumerated as “grand children”
Orphaned children were not enumerated as "orphan"
1850 is the 1st census that shows all family members
1880 is the 1st census that shows parental birthplaces and family relationships +++
TRY - Find a grave – FREE SITE - volunteer site all states; frequently has headstone pic
DO NOT SEARCH FOR A MARRIED WOMAN USING HER MAIDEN NAME.http://www.worldvitalrecords.com/
Try Vital Records – Birth, Marriage, & Death, Social Security Info., Census Records – FREE ALL STATEShttp://search.labs.familysearch.org/
Michigan did not require “by law” birth, marriage & death registrations until 1867.
Name: John Ryan
Age in 1860: 29
Birth Year: abt 1831
Home in 1860: Saginaw, Saginaw, Michigan
Post Office: East Saginaw
John Ryan 29, IRE - plasterer
Ellen Ryan 28, IRE 
Agnes Ryan 3, MI
Anna Ryan 1, MI
Bridget Maher 24, IRE - servant
Name: Ellen Mahrer [note spelling]
Age in 1870: 35
Birth Year: abt 1835
Home in 1870: East Saginaw Ward 2, Saginaw, Michigan
Post Office: East Saginaw
William Mahrer 27, IRE - mason
Ellen Mahrer 35, IRE
Agnes Ryan 13, MI 
Annie Ryan 11, MI 
John Ryan 8, MI 
Willie Maher 1, MI
Name: Ellen Mahn [AKA = Maher]
Birth Year: abt 1840
Home in 1880: East Saginaw, Saginaw, Michigan
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: William Mahn
Father's Birthplace: Ireland
Mother's Birthplace: Ireland
Occupation: Keeping House
William Mahn 37
Ellen Mahn 40
William Mahn 11
Ellen Mahn 8