Hi,
There are very few, if any, lists of passengers arriving in Newfoundland from Ireland. Since we were a British colony, no immigration permission was required and therefore no records were kept.
By the way I just discovered that a T. Cunningham was mentioned as a school teacher at Cape Broyle (south of Tors Cove) in the 1855 Report of Education for Ferryland District in the Journal of the House of Assembly of Newfoundland. Undoubtedly this was your Thomas Cunningham. Hopes this helps.
Kevin