Many of the sources cited above for the history of the African communities in Manchester also apply to the African-Caribbean communities. A much broader overview of the subject can be found in Jo Stanley's article, 'Mangoes to Moss Side: Caribbean Migration to Manchester in the 1950s and 1960s' (Manchester Region History Review, vol. 16, 2002-03 - pdf file).
There is also the publication 'Rude Awakening: African / Caribbean settlers in Manchester: an account' (Roots Oral History Project, 1992). This is based on interviews from the 1970s. Unfortunately we do not have a copy of this book at present, but the Race Relations Resource Centre do.
The autobiography of Whit Stennett, Lord Mayor of Trafford in 2003-04, entitled 'A Bittersweet Journey' (352.160942 STE), is also useful in showing the experiences of an immigrant from Jamaica who arrived here in 1959. It deals with his early life in Jamaica, his work in Manchester for the GPO, and his cricketing experiences in England, amongst other topics.
Novels can also be a potential source, because the authors may draw on their experiences of their community. One example is Joe Pemberton's 'Forever And Ever Amen'. This tells the story of a young boy growing up in Moss Side at the end of the 1960's but with references back to St Kitts where his family had come from. Please see the educational resource 'Picture Book Moss Side' which links extracts from this book to photographic images of Moss Side at this time.
Reference to West Indians is also made in the Manchester Evening Chronicle 1958 series 'Strangers in our Midst'.
Manchester Archives Flickr photostream
The photographs above can also be viewed directly on the Flickr site where you will find many more sets on Manchester Archives Flickr photostream.