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I may as well list my best sources. The best is of course the Family Register, a soft leather-covered account book with marbled paper inside the covers. A photocopy of the entries is included in Appendix 1.
There is also Pat Wyatt's book:
Wyatt, Dora Patricia (1984) Don't write a book about mother
The Latter Day Saints (LDS) have almost all the old parish registers on microfilm. By far the most useful LDS microfilms are:
1291763 & 1291764 - Parish Register Transcripts 1722-1825 Kingston Parish
Oh, if only I had time to analyse that data in more detail.
1291764 also contains the much less useful 1851-1859.
The next most useful LDS microfilms are:
1291698 & 1291699 - Parish Register Transcripts 1664-1826 St Andrew Parish
1291698 also contains a name index for 1664-1870
I've also read:
1291768 & 1291769 - Parish Register Transcripts 1725-1835 Port Royal Parish and index to 1868
Contains the marriages of Christian Boom & Dorothy Harrison, and of John Hall & Allegonda Boom, but not very much else.
And:
1291711 - Parish Register Transcripts (all Parishes) Baptisms 1826-1834
1291727 - Parish Register Transcripts (misc. Parishes) Marriages 1826-1839
I read through the Kingston, St Andrew & St Thomas in the Vale Parish records in these. The Kingston marriages stop in 1836.
Of other sources, I've browsed:
Philip Wright (1966) Monumental Inscriptions of Jamaica.
and:
Hollis Hallett, CFE (1898) Bermuda index, 1784 - 1914: an index of births, marriages, deaths, as recorded in Bermuda newspapers.
There are many sources that I haven't seen (it's up to you now):
Some sources contain heaps more information but would be a headache to wade through.
The LDS has Kingston Parish Registers for 1837 to 1848 (LDS film 1291765) and 1846 to 1851 (LDS film 1291766). It also has some other parishes including Saint Thomas in the Vale 1816 to 1826 (index to 1869) (LDS film 1291678). There are miscellaneous Jamaica baptism, marriage and burial records for 1826+ to 1834+ (LDS films 1291712 etc., 1291728 etc., 1291731 etc.). If I take this further, I'll definitely look at films 1291765 and 1291731.
I've recently become aware of two more LDS films. Most of the family names on the Family Register have been copied onto Film 1438890 (unfortunately this has Boone instead of Boom and some other mistakes). Some further information on the Astwood, Handasyde and Adamson families in Australia is on Film 1553193. Both are indexed on the IGI.
Some sources may or may not contain useful information; I'd like to see a table of contents or know more about these first:
Feurtado W.A. Official
& Other Personages of Jamaica, from 1655 to 1790.
(described as "a mine of misinformation").
Higman B.W. Jamaica Surveyed: Plantation maps and plans of the eighteenth and nineteenth centuries.
(only a few of the hundreds of maps available in Jamaican libraries. James W Lee has a collection of ancient maps).
Oliver, Vere Langford Caribbeana Vols I - VI Pedigrees of early families of the Caribbean.
(some but not all volumes of this are microfilmed by the LDS).
There are many other sources, a trip around the web will net hundreds of book titles ranging from travel guides to histories of slavery.
There are also some hints that other really valuable sources may exist. To start, Pat Wyatt's sources are somewhere. There are also Wills, Almanacs and Census records. You can pay Jamaican researchers to search for Wills, and Pat Wyatt has. The 1840 Almanac is on the web but I think that others exist. There was a Census in Jamaica in 1844 but I don't know what records were kept.