You may be lucky and someone will recognise the family however I'd suggest
(a) get in touch with Social serives on the Island (not sure if you are on or off Island) - they should have the records of children in care for this period (I have records but none past 1905) - that should allow you to get birth certificates
(b) get marriage certificate of James + Margaret Corlett - that should give their ages + parents - it is likely that James would be in the 1901 census after which usually easy to take back to 1800's