The Virgin Islands as they are officially known are usually referred to as the British Virgin Islands ("BVI") to distinguish them from the neighbouring US Virgin Islands. You may even have heard of the Spanish Virgin Islands, which far from belonging to Spain form a part of Puerto Rico, and/or the Danish Virgin Islands (more properly, the Danish West Indies). Denmark sold the latter to the United States in 1916 whence they became the US Virgin Islands.
The British part of the (unofficial) name also correctly alludes to the fact that the islands are a British overseas territory. With the naming issues hopefully addressed, we can now look at IP on the islands.
As a non-sovereign nation it is unable to sign up to International organisations and treaties; that remains the responsibility of the United Kingdom.
The Registry of Corporate Affairs, a part of the British Virgin Islands Financial Services Commission, oversees the administration of IP rights. Unfortunately, there is a real lack of any IP information on their website.
Substantive (independent) trade mark applications are possible. These must be filed using the former British classification system, which you may recall is still used by The Bahamas. It is also possible to register (extend) trade marks based on UK registrations. These will replicate a UK registration's particulars including the specification and classification. Currently, the UK extension route is the only one available in which to register service marks.
The local Government are planning on introducing new trade mark legislation. You will see that this is a modern law meeting international standards (e.g. provisions for well-known marks, priority, multi-class applications, etc.). It does not contain any provision for the Madrid Protocol. The BVI Government are not in a position to accede to the Madrid Protocol, but the United Kingdom could do so on their behalf if they were specifically requested to do so by the BVI Government. I feel this is a disappointing oversight bearing in mind I believe the BVI Registrar has been a member of INTA and should be aware of international agreements in relation to trade marks.
When it comes to designs I believe UK registrations cover the BVI automatically, although if the jurisdiction is of importance it is recommended to have a local 'confirmatory' Cautionary Notice published too. However, Registered Community Designs should not provide protection. UK patents can be extended to the BVI but this must be done within three years of the UK date of issue (this includes European patents valid in the UK).
A new trade mark law will greatly simplify this area and make it easier for North American applicants, in particular, to register their trade marks. Despite being a British overseas territory the BVI's geographical proximity to the likes of the US is obvious. The islands also use the US dollar as their currency.