There may be whole classes of songs that would seem to generally meet the criteria posed -of unknown authorship but written originally in 19th century. I am thinking here of Irish emigration songs, transportation songs (Australia) as well as perhaps the majority of songs coming out of Australia. Perhaps bothy songs as well (for example, Bogie's Bonny Belle has been attributed to the mid 1800's). Still, the authentication could be the problem - demonstrating conclusively that the songs in question had no antecedents before the 19th century. So I think that Phil's initial question is an interesting one but it could be a bear to research a bunch of specific songs.