This is, perhaps, not really surprising, since,
when the school petered out in the early 20th
century, it apparently left no records, and no successor. Virtually the only records of its
history are in the contemporary newspapers.

Nevertheless, the Collegiate School educated a majority of the men, of all colours, who became prominent in Jamaican life well into the first half
of the 20th century.

The Editor of the Colonial Standard was inspired to
write on education in Jamaica by the establishment
of a secondary school for boys by a group of Jesuit
exiles from Columbia. The start of the St George's College in September 1850 stimulated some very
hostile reactions, inspired in part by a long tradition
of fear of Jesuit activities among Protestants. There
was also protest from schoolmasters in Kingston,
especially Nathaniel Melhado and Solomon Meyers
both of whom claimed to offer a classical curriculum
in their schools.
The Editor was not impressed:

In spite of Mr Nathaniel Melhado's continental
education and Mr Solomon Meyer's sententious
laudation, we maintain that up to the present hour
it has been impossible for any gentleman to give
his child  a 'finished classical education' in Jamaica.

If Mr Meyers wishes to know what we mean by a
'finished education,' we may say  that we mean a knowledge of the upper walks of Greek and Latin literature. We should like to see a child who has
been turned out of either seminary who could take his stand in an upper form at Eton or Harrow, or who could take his 'little go'* at either University.
(Colonial Standard, September 4, 1850)

*'little go'

The only major school in Kingston which provided secondary education for boys in the 1850s was Wolmer's, which had apparently given up the teaching of Greek and Latin as irrelevant to local students. Wolmer's became almost entirely an elementary school from 1867, until the reorganisation by the Schools' Commission in the 1890s. Until the Jamaica High School was moved from Walton Pen in St Ann into Kingston in the 1880s, St George's, where the pupils were mostly Roman Catholic, and  the Collegiate School, founded in 1853, were the only schools offering a secondary and classical education for boys in the city.

Sources:
http://en.wikipedia.org/wiki/Jamaica_College

History of the Catholic Church in Jamaica,
Francis J Osborne, S J, 1988

The Legacy of a Goldsmith: A History of  Wolmer's  Schools  1729-2003,
Patrick E Bryan, 2004