The marriage of William Cowin and Isabella Cubbin seems to have been registered in Birkenhead Registration District in 1878:
The certificate should get you her father's name. You can then check on FamilySearch for the baptism record on the Isle of Man.
There is a useful guide here:
The only example I have obtained is for a birth (1946) and on that the information is exactly what I would expect from a register entry in England/Wales of the same era.