The family appear in the 1841, 1851 & 1861 censuses, in the latter two of which Elizabeth is given as Liverpool born.

In 1841, there are two children, Elizabeth aged 3 (so dob is c1838), and John aged 1 (dob 1840).

FreeBMD gives two possible refernces for Elizabeth:
Kewley, Elizabeth, GRO Dec 1837 Liverpool 20 178, and Kewley Female, GRO Sep 1838, West Derby 20 862.

A promising reference for John is:
Kewley, John, GRO Sep 1840 Liverpool 20 389.

The birth cert for either would give you Elizabeth snr's maiden name thus possibly helping you to home in on the marriage details.