The banjo played a central place in the popular music known as Jamaican mento. Ethnomusicologist Dan Neely has written an excellent dissertation about this music, which you can purchase from University Microfilms.
The documentary film “Pimento and Hot Pepper: The Story of Mento Music” does a nice job of exploring the history of this music. You can see the trailer, which includes some nice excerpts of mento banjo, below.
When he was doing fieldwork in Jamaica in the late 1950s, anthropologist Sidney Mintz collected a banjo of unique construction: you can read more about this here.
Though mento is, today, not as popular as it once was, many Jamaican musicians continue to play the banjo in a variety of settings. Ken Bilby, a leading ethnomusicologist of Caribbean music, has also shared the photographs below of contemporary banjo players in Jamaica.
The banjo has also been a part of popular music in many other parts of the Caribbean, for instance in St. Lucia. The photograph below, taken in 1972, is of a St. Lucian group called the “Banjo Man Players,” for instance.