If Thomas Craine was a private tutor in Liverpool then Gore's directory for Liverpool would have his address (they may be on microfilm accessible in the US - they are at Liverpool PRO and Manx Museum has a copy I believe) - then you could find entry in 1841 Liverpool Census - looks as if you are searching for a family that moved to Liverpool in early 1800's (? after 1815 when things started to go wrong on the Island) or possibly before - there are several Crane's (but no Craine's) in my 1796 Gore's directory).