I've not fished Tobago but being located in the southern Carribean I would say your chances of finding fish are very good. Barracuda should be plentiful and are great on fly rods. Bonefish should be there but this would depend on wether the local fishermen net them for lobster bait - sadly this is the case on many of the Bahamian Islands where fly fishing is undeveloped. Permit have a habit of doing their own thing and generally turn up when you least expect them. Tarpon are a possibility but tend to be seasonal. Accross the carribean in the southern Yucatan, they can be found casting in the surf during July. If you can't find a local guide, I would try to hire a local fisherman to guide you for a day. He'll probably think you're crazy but local knowledge is gold in situations like this.
Let us know how you get on - It's always good to hear pioneering reports!