Jeff, to find a gravestone the first thing to do is to establish when they died, from likely entries on FreeBMD or paid sites like Ancestry or Findmypast.
Start looking from the date of the last census in which they appeared, or other public record (but bear in mind that PO and other directories are usually a couple of years out of date, as are electoral rolls).
You may need to buy more than one death cert to find the right person.
Then you need to check for records of cemeteries close to their address.

It is important to find all possible information about each generation before searching back to the previous one, to avoid guessing.

Looking again at your ones, I wrote that Elizabeth 54 Plain Sewer of 5, Whitemill Street, Liverpool, was a widow in the 1861 census. So husband Robert died between the 1851 census and the 1861 one. As Elizabeth was still in Liverpool in 1861 it is likely that Robert died there.
Possibilities are:
Deaths Dec quarter 1857 (Oct/Nov/Dec)
Surname First name(s) Age District Vol Page
Goldsmith Robert Liverpool 8b 96
............
Deaths Jun quarter 1859 (April/May/June)
GOLDSMITH Robert Liverpool 8b 23

Ages were not given at that time.

I couldn't find Elizabeth in the 1871 census.
Possibility is:
Deaths Dec quarter 1869 ((Oct/Nov/Dec)
Surname First name(s) Age District Vol Page
Goldsmith Elizabeth 58 Liverpool 8b 193

Her age of 58 could be because some people gave varying ages as they grew older. It is not far from her age given in 1851.

If you buy her death cert., and trace her burial from that, you may find them both in the same plot. Or if you live locally, try the local record office, and phoning the cemeteries near their 1851/1861 addresses.

Sue