Barkly House/Clarendon Hall
The earliest reference to Barkly House/Hall I have found so far is in 1860, in the New Monthly Magazine published in London; the reference comes in one of many quotations from Anthony Trollope's book, The West Indies and the Spanish Main, in an article about travel in Cetral America and the West Indies. The linking of Barkly Hall with Date-tree Hall and Blundle's Hall would seem to indicate that it had a well-established reputation.
in the Gleaner, on page two -