Well, as you point out, one clear category of songs that fit this requirement are songs commemorating a historical event that did not happen before the 19th century. For example, again from the Irish tradition, songs about Robert Emmett or the Manchester Martyrs. Otherwise, it is harder to prove a negative - i.e., that a song whose authorship is not conclusively known was not written before the 19th century. One that I think meets your requirements is Spencer The Rover. I will try to think about others.
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