I have found no pictures of waggonettes in Jamaica
in the late 19th century, but they probably looked like this.

waggonettes

from Jamaican Song and Story, edited by Walter Jekyll, 1907


What was a waggonette?
Daily Gleaner, October 14, 1888
   Clearly it appeared to some business men that there was room for a city transport service to supplement the street car lines.  The waggonettes could also be used for trips out of Kingston.

Daily Gleaner, December 29, 1888
The Company started to set up its operations  in January, 1889:
Daily Gleaner, March 25, 1889





Waggonette Crescent, on the site of the Waggonette Company's headquarters,
is still there, between East Street and Kingston Gardens.