The departing ships were noted in the Liverpool press but merely date and captain, destination (+ line where appropriate) - no index exists - when I was 'doing' the much easier 1826/8 departures it required a day wading through microfilmed newspapers at Liverpool Central Library - luckily the films were considerably better than those of the Manx press in Manx Museum so not too bad
Remember that they could be to New Orleans and also Canada - have a look at my emigration pages http://www.ee.surrey.ac.uk/Contrib/manx/famhist/genealgy/emig.htm