It is hard to be certain this is the right family - James & Susannah's ages & relationship are the only things that agree with the 1871 census. It may be that Ancestry (which I use) has indexed the family wrongly which would make it very difficult to trace them.

I went back to the IGI and to my surprise found this time a James Williams son of James Williams and Ann Jane being christened at St Barnabas, Douglas, on 7th Dec 1856. Not Port Erin, but at least it's the Isle of Man. I then tried searching on children of James Williams and Ann Jane in the hopes that Suzanna would turn up. She didn't, but Margaret Annie Williams c. 19 Nov 1854 at St Matthew's Douglas did. Yes I did look for her in 1861 but, you guessed it, can't find her either. A look at the St Barnabas baptismal register might give you some more information that would help identify this family, for example father's occupation or address, maybe even 'of Liverpool' if you're lucky.

Have you tried looking for an online index of Liverpool burials for the elder James? I've a feeling I came across a site where someone was posting memorial inscriptions, either for Anfield or Everton I can't remember which. Or you could try a Liverpool/Lancashire forum - must be one. Finding an inscription could be a bit of a needle & haystack job though with such a common name and no precise death date. If you know James junior's death date, though, they might be buried near each other?

It's looks like we've come to the end of the 'easy' part of this research, and I think I'm well and truly out of my depth! Certainly out of ideas anyway.

Sorry can't be more help - hopefully someone more knowlegeable will jump into the thread and be able to offer something useful!
Good luck, Sylvia