Before 1837, when civil registration began, parish records did not state names of parents on marriages - usually just the status of the bride and groom (but sometimes not even that the further back you go), whether of the parish or elsewhere (again, not always shown) and the names of witnesses.
The information gleaned from the census shows what you need to look for.
Joseph Merrett is shown to be bc.1813-1821 Dauntsey, depending on which census you look at - I personally think he was born c.1817 like Elizabeth (shown born 1818 when he died in 1884) but you would need to get this checked in the Dauntsey parish records (records for this parish aren't online for this period I'm afraid - I did see that some public trees on Ancestry show him to be the son of a Thomas and Rachel but with nothing to substantiate it and I personally think they are wrong. I found a transcript of Dauntsey parish records but they only go up to 1812. A Thomas and Rachel had 3 sons 1790, 1793 (a Joseph) and 1797 but nothing shown after.
As to Elizabeth Harding bc.1813 (?) Christian Malford.
1851 Census, Christian Malford (ref.HO107 - 1836 - 750 - 5)
Joseph Merrett 38 Railway Lab. b. Dauntsey
Elizabeth Merrett 38 b. Christian Malford
Francis Merrett 13 ditto
Jane Merrett 11 ditto
Matilda Merrett 8 ditto
John Merrett 4 ditto
Anne Merrett 1 ditto
Richard Harding father-in-law 75 Pauper formerly Carpenter b. Kemball (Kemble)
+ a lodger
So, Elizabeth's father was a Richard.
Elizabeth Harding was bp.4/4/1817 Christian Malford (a little later than 1851 Census suggests), dau. of Richard Harding and wife Anne. (Joseph and family living with Richard and Ann in 1841 - Joseph and Elizabeth both shown as 20 but ages were rounded down in 1841 which means they could have been born anywhere between 1816-1821).
You can probably find out more on the Harding's at Christian Marlford on familysearch
but will need to establish where records for Dauntsey are held after 1812 (Wiltshire Record Office?) and duly make a search for a Joseph Merrett bc.1817-18.
Hope this helps.
Annette