I am having trouble finding out who Starbuck's competition would be if they expanded to Trinidad and Tobago.
Try looking up the Starbucks report using Marketline Advantage (found from the Company and Industry Resources tab) you will get a list of competitors, including potential international competitors. This will not help you find specific competitors within Trinidad and Tobago, but it will certainly be a better starting place.
For competitors more specific to the region, you may want to start looking in some of our other databases, such as ABI/INFORM Complete and Business Source Complete (both on the same list of databases as Marketline Advantage and hoovers). These tend to provide information in the form of journal articles and newspaper articles, however occassionally you will find an industry report.
I found one generally on the Food and Drinks industry for the Carribbean. - https://ezproxy.uhd.edu/login?url=http://search.proquest.com/docview/1448572797?accountid=7109
While it does not speak specifically to coffee shops, they are mentioned throughout the document and will give you a starting place for regional competition.
Otherwise, in these two databases, try searches such as:
Trinidad AND tobago AND coffee shops
Carribbean AND coffee AND retail
You may even want to try:
Trinidad AND Tobago AND starbucks