The information I have found on the family of the Rev C L Barnes is very limited, but certainly further research in the records of births, marriages and deaths for the relevant period will yield more facts.
I have found no record of his birth (c 1841), but on December 10, 1873, he married Matilda Elizabeth Jacobs, of Kingston. The marriage was performed by the Rev G W Downer and the witnesses were George A Barnes (presumably a relative, possibly a brother) and R M Whittle (perhaps a fellow student mentioned by Evans).
I have found record of the births of three children in Pratville, in Manchester: Matilda Elizabeth Ann on March 7 1879; twin boy and girl on August 27, 1885, the witness to their birth being Joseph I Barnes, possibly an uncle.
It is clear that Barnes' wife had died before his death in 1889. (There is an item listed in the National Library of Jamaica, Nuttall Collection, which I have not been able to see: it is noted in MS 209 Typed list of items - box 2: p7 357 letter from C L Barnes re his wife August 1886 [possibly referring to her death]) The account in the church newspaper indicates a large family of children to be provided for.
One of the Rev C L Barnes' sons was almost certainly Prof Christopher Lipscombe Barnes a prominent Black musician and business man, who died in 1965.