You have a very specific problem or at least request and I am not going to be able to solve it nor would I think many of the regular respondents to this particular site.
I am going to suggest that you itemise all the things that you regard as important to your quest such as:.....Caribbean, ....Itinerary,...Single Berth, .....Budget, ...... Length of cruise, ...... Timetable,...... Important needs, ...etc. etc. and ring as many freephone numbers as you can and see what they suggest and which gives you most ticks. I'm not trying to be awkward or evasive but this sort of task is done by many of us to find what suits our needs and the same thing should apply to you but your needs are different to mine and to a lot of others so it is one where you will get the best results by doing your own "legwork" and with that I wish you well. .......Neil
Try fred olsen or Thomson as they have some cheap deals and they may even have some single cabins left aswell. they only go to the caribbean early part of the year so you could possibly get a late deal. if you go to www.cruises.co.uk and then fred olsen and then down the right side single travellers there are some useful sites and agents mentioned. hope this helps.