Martinique Conure (Psittacara sp.)
It’s a fact that parakeets of the genus Psittacara (formerly included in the genus Aratinga) inhabit the islands of the Greater Antilles, where several species still occur on the islands of Cuba, Hispaniola, Jamaica and Puerto Rico; at least one additional subfossil form is known from the island of Barbuda in the Lesser Antilles, which makes it likely that others were once distributed on the islands inbetween.
Again, some other forms are known from accounts only, and some of these accounts are rather scanty and unfortunately sometimes not very trustworthy.
The Martinique Conure, however, is known from the description given by M.-J. Brisson in 1760, which again, apparently refers to a description and depiction by George Edwards from 1751 (see below).
G. Edwards in his description just writes:
“… My Friend for whom I made the Draught, told me, the Bird was brought from the West-Indies. …” 
And then, M.-J. Brisson states:
“Habitat in Martinique & variis Americae regionibus“
“Lives in Martinique and various American regions“
The bird depicted here is a Brown-throated Parakeet (Eupsittula pertinax (L.)), which occurs naturally with about 14 subspecies in northern South America as well as on many of the small islands off the northern coast of Venezuela, but cannot be assigned to any of the known subspecies without any doubt whatsoever.
There is now the possibility that this species was once much more widespread and might indeed have inhabited some of the islands of the Lesser Antilles, but I personally think that the parakeet depicted here was just caught somewhere on the South American mainland and was then brought to the West Indies from where again it was purchased by the person in whose possession it was when G. Edwards described and drew it.
If the island of Martinique ever harbored an endemic species of parakeet it probably was more closely realted to the more or less plain green (with a little red) species from the genus Psittacara known from subfossil remains from Barbuda, and found still being alive in the Greater Antilles.
 George Edwards: A natural history of uncommon birds: and of some other rare and undescribed animals, quadrupedes, fishes, reptiles, insects, &, exhibited in two hundred and ten copper-plates, from designs copied immediately from nature, and curiously coloured after life, with a full and accurate description of each figure, to which is added A brief and general idea of drawing and painting in water-colours; with instructions for etching on copper with aqua fortis; likewise some thoughts on the passage of birds; and additions to many subjects described in this work. London: printed for the author, at the College of Physicians in Warwick-Lane 1743-1751
 Mathurin-Jaques Brisson: Ornithologie, ou, Méthode contenant la division des oiseaux en ordres, sections, genres, especes & leurs variétés: a laquelle on a joint une description exacte de chaque espece, avec les citations des auteurs qui en ont traité, les noms quils leur ont donnés, ceux que leur ont donnés les différentes nations, & les noms vulgaires. Parisiis: Ad Ripam Augustinorum, apud Cl. Joannem-Baptistam Bauche, bibliopolam, ad Insigne S. Genovesae, & S. Joannis in Deserto 1760