Hello SDH,
I've looked through the Newington, (Sittingbourne) census for 1841, 1851 and 1861. It's not that big a place, and I can't find anyone that you've mentioned. If you've got the family on a later census, could you post the full transcript, which will give me birth dates of the children. Also do you know when and where James and Harriet were married, as I'd guess it was probably after the 1841 census. Any extra info that you can give will help narrow down the search.
Thanks,
Carol.