matt

This is what The Fiddler's Companion has to say: Fair Mary Mulholland:

O'Neill identifies the tune as the air of a County Down folk song, learned by O'Neill's assistant, Sergeant James O'Neill (no relation), from his mother. The original title was unknown so the compilers named it for James's mother.

So you may have to rely on someone recognising the tune rather than the name.

Mick