I think that your John Cox could be the one living at 3 Macdonald Street, Birmingham on the 1881 census with his parents and siblings;
William Cox 40 Cane pipe maker
Caroline " 39
Caroline " Daut 19 Nail cutter
William " Son 18 Fender Caster
JOHN " Son 14 " "
Frederick " " 11 Scholar
Rose " Daut 6 "
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On the 1901 census John and Isabella have children, their first born being Frederick. John's occupation is shown as a Malleble Iron Caster.
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John's baptism is shown on the IGI at the Holy Trinity church Bordesley, 30 January 1867. Father, William, Mother, Caroline.
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Of course this is guess work, but the pieces seem to fit.
Regards
Steve