How do I find records of people leaving Wales for Newfoundland (British colony) in the mid 1800's?

Records of my ancestors' marriages & births in Newfoundland were lost at sea; I thought I'd try looking at Welsh emigration or passenger lists if they exist? Any help is much appreciated with this dead end.

Thomas Matthews (b abt 1832) m Mary Davies; son James Matthews (b abt 1847); all 3 born in Wales.

James (Jamie) emigrated to Newfoundland, possibly with parents, possibly on his own. He married Elidiath Hicks in Newfoundland. Their son, George Llewellyn Matthews, is my grandfather.

thanks in advance for any help,
Donna Henley