Thanks, Geoff, especially for the Bonner article.

Clifford Leach, "Bottoms Up!" (1935), notes "To same tune as 'Samuel Hall.'"

Liza Carthy sings Waterson Carthy's rifacimento on "Fishes & Fine Yellow Sand," Topic TSCD542, 2004.

The Golden Ring also recorded a version in the ‘70s.

Pete Seeger and Alex Campbell used the tune of "Admiral Benbow."

The original tune (1701) was known as "Coming Down." A midi and two broadside texts of the song (and more) are here:

https://web.archive.org/web/20110723082022/http://www.davidkidd.net/Captain_Kidd_Lyrics.html