Well I've had another look in 'the book'. A whaleship Diamond (of Aberdeen!), commanded by Captain Thompson was wrecked in the ice in 1819 after taking 8 whales. I haven't yet found any other Diamonds so I think that this is the vessel we're looking for. The Diamond (371 tons and owned by the Aberdeen Whale Fishing Company had joined the fleet in 1812 under the command of Captain Moffat.
There were ships called Resolution (of Peterhead - which was wrecked in the ice in 1830), Eliza Swan (of Montrose) and Rattler (of Leith, also lost in 1819) fishing in the years 1812-1819. There are other Resolutions mentioned, one from Whitby and another (later, a replacement?) from Peterhead.
Of interest to our US friends, the Eliza Swan was captured by USS President (Commodore Rodgers) on 24 July 1813 and ransomed for £5000, and sent back to Montrose with the crews of two other Engish ships that Rodgers had captured.
In spite of all bravado of the song (incidentally, my brother's favourite), the Diamond did not have a very spectacular career.
I can recommend the Basil Lubbock book. It's chock full of information culled from many sources and deals with each season in turn. It dates from 1937 (mine is a Brown, Son and Ferguson reprint of 1978). I can also recommend the excellent Maritime Museum here in Hull, with a large section devoted to the Greenland Trade (whaling). Hull was for many years the main supplier of ships and men to this trade, and there's plenty to see in this section of the museum.
Les from Hull (doing his bit for Hull's tourist industry)