Ships of the Royal Navy gives 13 vessels served under that name in the Royal Navy, and some have been used in the Leeward Islands. So very difficult to find which was depict on this stamp.
But I think I found the ship which most probably was depict on this stamp, and who has a connection with Grenadines of St Vincent. Also Navucula has the same info for this ship.
In 1795 -96 a second Carib-Carifuna/British war erupted in St Vincent in response to British failure to honor the treaties.
14 March 1795 the Caribs Chief Joseph Chatoyer is killed in battle and by 1796 the Caribs had to negotiate a peace.
The majority of Caribs were then sent to a small island of Balliceaux in the Grenadines and later to Bequia.
25 February 1797, some 5000 Caribs (mostly Garifunas) were loaded on the HMS EXPERIMENT under command of Capt Barrett and two other British warships and then transported to the island of Raotan (Rattan) off the coast of Honduras.
She was built by Robert Fabian, East Cowes for the Royal Navy.
13 July 1780 ordered.
June 1781 laid down.
27 November 1784 launched under the name HMS EXPERIMENT one of the Roebuck class.
Tonnage 890 ton (bm), dim. 140 x 38 x 16.4ft.
Armament 20 – 18 pdr under deck, 22 – 12 pdr. upper deck, 2 – 6 pdr. forecastle.
Crew 200, as troopship 155.
06 February 1784 completed. Building cost £12.348 without outfitting..
11 January 1785 at Portsmouth, where she was coppered and fitted out as a troopship.
January 1793 commissioned as troopship under command of Comdr. Simon Miller; 26 November 1793 left for the Leeward Islands in the Caribbean.
After arrival there used as storeship.
January 1795 under command of Cmdr. Lancelot Skynner, August the same year command was taken over by John Barrett.
November 1797 returned to the U.K.
Refitted at Deptford from February till May 1798.
February 1798 recommissioned under command of Comdr. John Saville as troopship.
February 1801 sailed for the Mediterranean, used in the Egypt operation during 1801.
January 1802 under command of Cmdr. George Mackenzie, still in the Mediterranean till November 1803 when she returned to the U.K.
December 1803 in use as a guardship at Lymington till January 1805.
May 1805 under command of Lieut. Robert Yule.
From July till October 1805 fitted out at Portsmouth as a harbour storeship for Falmouth.
August 1805 under command of Lieut. William Stewart, followed by a few others till 1814.
1814 In ordinary at Portsmouth.
July 1815 fitted out as “lazaretto” for Liverpool, where she lay as a floating lazaretto from 1817 till 1834.
08 September 1836 sold for £1.420, most probably for breaking up.
The Grenadines of St Vincent 1982 1c sg208, scott222
Source: some websites. Ships of the Royal Navy by Colledge.
British Warships in the Age of Sail 1793-1817 by Rif Winfield.