Do you have them in the 1901 census ?...this should state their place of birth which will give you a start ?
could this be them - Canal Street - sub district Aspull,Standish ,Wigan
Patrick Duffy aged 28 - born Ireland
Mary Duffy aged 28 born Blackrod ,Lancs
Mary aged 1 b Standish
if it is a possible you are looking for Mary McMahon b 1872/73 in Blackrod
there is a Mary McMahon b 1873 Hindley,Wigan - mmn McMahon - Blackrod on Wiki comes under Wigan Poor Law Union
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ADDED
www.lancashirebmd.org.uk1898 Rose DUFFY - mothers maiden name McMahon - Standish district STND/34/416
1899 Mary Duffy - ditto ..................................................................STND/35/440
1907 Catherine DUFFY ditto.............................................................STND/41/198
...
1901 Agnes DUFFY - mmn McMahon Aspull district ASPL/56/189
1904 Alice DUFFY - ditto ..................................................................ASPL/59/72
So it looks like 2 Duffy / McMahon families in Wigan - unless they moved from Standish to Aspull then back again
the 1911 census will tell you if they are seperate families or one family