The ship was commissioned as a privateer in Belfast in 1778 and made two voyages, the first under Captain Robert Moore returned unfought and prizeless after six months. The second, under Capt George Colvill fought the battle described. The song probably derives from reports in the Belfast Newsletter on 5 November 1779. On return from this voyage in February 1780, the ship arrived at Donaghadee on Belfast Lough to land some crew and took on local men to work to Belfast. Unfortunately, they were caught on a lee shore and driven into Ballyhome Bay. All on board drowned. George Colvill's grave with a notable gravestone, now unfortunately shattered, is in Bangor Abbey graveyard. A six-pounder cannon with a plaque identifying it as having been salvaged from the Amazon, is outside.
The song exists in two forms - The Irish Privateer and The Spanish Snow. I transcribed the song from Robert Cinnamond's singing in mid 1971 and added a few lines. Kevin Mitchell recorded it from my singing and passed the song to Jim Mageean from whose record 'Of Ships and Men' Terry Timmins learned it. The performance that Kevin recorded lacked a verse:

Our ship she was rigged both fore and aft, a gallant craft was she,
Out flag was at the Topmast, before we put to sea,
Our Captain's name was Colcill and our ship the Amazon
And the most of our brave heroes were reared near Belfast Town.

The song has an interesting printing history part of which is outlined in one of the Dungbeetle articles on the Musical Traditions website.

I could send a more detailed account from my PhD thesis to any who request it. jmoul81075 [at] aol.com