There is assuredly a traditional Granuaile song, collected in Minnesota in the United States, of all places. It's not the same as the Granuaile song cited above. The American version was collected by Bessie Stanchfield from Elma Snyder McDowell of Saint Cloud. She published the text in California Folklore Quarterly, Volume 4, #4. (October 1945), as "Old Granny Wales." Neither she nor any of the (American) folklorists she consulted recognized it as being about Granuiale. Her version begins:

Old Granny she rose in the morning so soon
She slipped on her petticoat, apron, and gown
Saying, "Very bad news last night came to me,
They're wronging my children that's o'er the sea."

Old Granny then mounted her gelding in haste,
And to fair London city -- it was her first place,
As she was prancing up fair London street
'Twas there with Lord Cornwall she chanced for to meet.

Stanchfield did not print the tune, but she collected one. It's in her papers in the Minnesota Historical Society archives. I do not believe her transcription accurate; I made an attempt to correct it on the Minnesota Heritage Songbook site. It is Roud #2817 (a version got filed as #15026). In addition to the Minnesota collection, Thompson found it in New York, and there are several songster versions.

The Chambers/O'Lochlainn song is Roud #3034, and I know of no field collections of that. Moylan and Zimmerman had another song, "The New Granuwale," that doesn't seem to have a Roud number; it doesn't have any field collections either. There is also Roud #3068, "Poor Old Granuaile," which isn't exactly about her; it's from the era of Daniel O'Connell. There are a few other Irish freedom songs that also mention her. Generally they aren't about Grace O'Malley (the "real" Granuaile) but about Granuaile as a symbol for Ireland.