Upvote:3
Based on the answer to How can an Indian citizen travel to Ecuador without a transit visa, it looks like you can do this by going India -> Amsterdam -> Paramaribo -> Trinidad and Tobago.
Upvote:4
Starting from the destination, Trinidad and Tobago has two airports with commercial services. Unfortunately, all the long-haul or transcontinental flights listed in the Wikipedia articles on Piarco International Airport and A.N.R. Robinson Airport go to countries where Indian citizens do need visas for transit (including the US, the UK, Canada and Germany) so there is no obvious solution here.
A route through another country in the Caribbean might work but I could not find any viable option, in particular because Indian citizens apparently need a visa in Suriname and in Saint-Martin/Sint-Marteen, both of which are served directly from Amsterdam Schiphol, where you could transit without visa.
Note that if you have a residence permit or visa for the US, Canada, Australia, New Zealand, Japan or a country in the EU, you might qualify for an exemption, e.g. in London or Frankfurt.