I think I have accidentally found James Christopher's first marriage. He is just James, a mariner, father James a surveyor. He married Maria HAY in Liverpool in 1869, batchelor and spinster, both of Brook Street, both full age, her father is James HAY, a shoemaker. Witnesses are John EAGAN? and Catherine KEHOE. James signed his name this time.
This child appears to be theirs...
CLARKE, JAMES
Mother's maiden surname: HAY
GRO Reference: 1869 J Quarter in LIVERPOOL Volume 08B Page 112
He was baptised at St Mary's Catholic Church, Liverpool, and mother's surname is recorded as HAYES.
Debra 
Just rechecking - the mother’s name has been transcribed as Hayes but the page shows Hay.
There is a note in Latin which indicates, I think, that the child was baptised at home as he was in danger of dying - ‘domi imminens periculum’ (or similar).
There is a Catholic burial at Ford Cemetery 7th August 1870
James Clarke, 15 months, 81 Dundas Street Bootle - no indication of family though.
However in 1871, there is a Patrick And Honora Clark living there so looks unlikely to be the same James.
It is frustrating that we can’t find William - or James Christopher.