Barbados was settled by the English in 1627, and became a center for the sugar industry. The island had a combination of slaves and indentured servants; both African and European. The Irish were an important piece of this trade in human bondage. Much has been written about the “Barbadosed” Irish, who were sent to the island as slaves under Oliver Cromwell: www.yale.edu/glc/tangledroots/Barbadosed.htm The number sent will never be known, but estimates range from 60,000 to 12,000.
For colonial Catholics, remember, this was a Protestant colony, so your ancestors will be found in the Anglican records. There were also Irish Moravians and Quakers on Barbados. Quakers can be traced to counties Leix (Queens) and Wicklow.
A useful reference work is Geraldine Lane, Tracing Ancestors in Barbados: A Practical Guide (2007) as well as numerous published and online articles. One handy article is Dwight A. Radford and Arden C. White’s article, “The Irish in Barbados,” in The Irish At Home and Abroad 2 (3) )1994/5): 92-97.
Major resources include James C. Brandow’s Genealogies of Barbados Families (1983) and JoAnne McRee’s six volume series Barbados Records(1979-1984). Much has also been preserved in Vere Langford Oliver’s Caribbeana and The Journal of the Barbados Museum and Historical Society. The core records can be found at the Barbados National Archives; the National Archives, Kew: www.nationalarchives.gov.uk with much on microfilm at the Family History Library: www.familysearch.org
For those of us with Irish colonial ancestry in the English colonies, whether white or black, Barbados is such as important link that we dare not ignore it.