The bird on the cover and frontispiece of both the 1936 first edition and 1947 edition is a male Cuban Tody.

If you examine the color illustration closely (above, left) on the 1936 edition,  you can see its nest hole. (The nest hole was cropped out in the 1947 edition.)

Here's Bond's writeup (Under range: Fidel Castro later changed the name of the Isle of Pines to the Isle of Youth):

More "Birds of the West Indies" blog posts here:

Yesterday: A terrific "Birds of the West Indies" webpage.

Wednesday: The two first editions of "The Birds of the West Indies."

Monday: Read the 1936 BOTWI online for free, here.

 Sunday: Ian Fleming's copy of BOTWI.