A new database of English settlers in Barbados from 1637-1800 is now on Ancestry.co.uk; it offers births, wills, marriages and other documents.
For those with Sephardic Caribbean ancestors, this database may be a goldmine of information.
I did a quick search for COHEN, and under an interestingly-named heading of "Jewish Baptisms," found numerous Jewish births. A page with dates of 1799-1800 held a transcribed, typed list of numerous births. The data comes from Register RL1/75. A further note indicates the register is in deteriorated condition and is closed to general view.
Names of infants and parents:
Isaac, son of Benjamin Henriques DaCosta
Joseph, son of Naphtali Hart
Benjamin and Mozeley, twin sons of Isaac Elkin
Walter and Isaac, twin sons of Jacob Levi
Daniel, son of Moses Pass
Sarah, daughter of Moses DeCastro
Hannah, daughter of Eleazer Myers
Sarah, daughter of Jacob Levi
Hananel, son of Moses Decastro
Isaac, son of Benjamin Cohen de Azevedo
Rebecca, daughter of Lemon Hart
Esther, daughter of Elieser Montefiore
HINT: Search for common Jewish given names, such as Isaac (or Isaque, as it is spelled in some documents), Jacob or Moses, and other families of Sephardic lineage will show up. Names with "de" sometimes run together; e.g. de Fonseca will be listed as defonseca or the Portuguese version, dafonseca. The documents also indicate relatives in different cities and daughters' married names.
Here's a will dated July 4, 1685, which was translated from Portuguese.
NAVARRO, Aaron, son of Abraham Navarro of Amsterdam, now resident in Barbados. Since there is no money in the business concern in Brazil, brother Moses Navarro should come to Amsterdam; Iihac Nunes Navarro - Adm in Brazil; my nieces, daus of Mandey Couzal; the heirs of bro Jacob Navaroo; Jacob Fundas; Samuel Frazad; Samuel DeNeiga (also spelled DeVeiga) regarding the care of Abraham Navarro or Mosso concerning the care of his heirs; mentions the Adm of bro Mahamad Eveham (?); daus Hanah Navarro and Ehetta Navarro; mentions Moses Hisquian DeMercado, wf Esther Navarro; chn Moses Navarro, Jacob Navarro, and Sarah Fletcher to place property with the heirs of my bro if own heirs die; Haham Reby; Elias Lopez; Jacob Dafonseca Valle; Joseph Senior; nephew Abraham Valverde; Nosea May Sarah Torres, chn of my wf (?) Esther Navarra. signed Aaron Navarro. Witnesses: Joseph Senior, Sam Brunts, Thomas Page, Jacob Baruh Louzada, Jacob Dafonsecca Neza. Proved 29 Oct 1685.
The 1711 will of merchant David Castello indicates his sons Jacob and Ephraim are to receive the 5 books of Moses he has in synagogue. His son Moses and daughter Hannah are to receive 1/3 of a house in Amsterdam near the Vinticue in the company "of my sisters which was put in the orphans house in Amsterdam by my fa [father] in 1670; daughter Judith Mandez, wife of Moses Mandez Jr - 5 shillings, and names his wife Rebecca as his executrix.
A 1715 document, a memo to a will, reveals that the person gave his nephew "420 aces in the parish of St. Marie's in Jamaica I bought of Moses Cohena, a Jew."