One of the worst places to search for records is Trinidad and Tobago. The system is archaic, they still rely on manual searches through large books that are falling apart. The certificates are also hand written too! No computerized stuff here at all save for the chit at the cashier. The other thing is the length of time it takes which is about one to two weeks if you are lucky.
It's not that hard in the UK provided that you know exactly what you are asking for, and go armed with every last bit of detail that is requested. If however you only know some of the facts, the information is near on impossible to get hold of, especially the older the dates the harder it gets. The more recent dates that you are searching do seem to be easier to access.