Have you found anything on freecen.rootsweb.com?
Cornelius Bice does not appear on the England 1861 or 1871 census index.
Is this him on the 1881 canada census?
Corneilus BRIGE M Male English 42 England Farmer Plymouth Bretheren
Mary J BRIGE M Female Irish 26 O <Ontario>
Elston BRIGE Male Canadian 2 O <Ontario>
Sarah BRIDGE Female Canadian 17 O <Ontario>
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Source Information:
Census Place Kingston, Frontenac, Ontario
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If it is, it certainly implies that he was also there in 1871 and probably for 1861 too.
Perhaps with additional information we may be able to direct you in your search.
Pauline