Hi Ruth,
It is possible that Eliza was away from her home at the time as she must have been very close to giving birth to William. Maybe she was in the Poorhouse Infirmary or somewhere llike that or perhaps even with her parents.
I have tried looking for William to see if he was born at the date of the census but nothing positive.
With the name being Davis or Davies and the inclusion of Monmouth into Gloucestershire records, you could find it very difficult to be sure of finding the right one.
It would be safer to buy the birth certificate for Eliza if you are sure the one you have identified is the right one and find the mother's maiden name from that. You can then search for the marriage details with more confidence.
I too had found those marriage entries but as the majority were in Bristol, I think Eliza would have said Bristol on the census and not Gloucestershire.
Not very helpful I'm afraid.
Best of luck,
Elizabeth