There is a flying club at the only airport Grantley Adams (?) .
I got an hour in 1999 with an instructor in a C152 - 8PLAB. They also had a couple of PA28's and some twins.
I couldnt get a solo, the story went ; you had to get a Barbados licence - that meant a check ride with an examiner + a small fee. As the only examiner was off the island during my stay it didnt happen.
Bit of forward planning should sort it, sorry dont have any contact data try Tourist office web site.