The following is lifted directly from http://www.misswardmusic.com/caribbean.html
Calypso: Originally the national dance of Trinidad and Tobago, calypso is particularly associated with carnival. It has:
- 4/4 time with syncopation
- acoustic and bass guitar or band with trumpets, saxophones, electric guitars, drum kit and Latin percussion
- often uses three-beat rhythms with two long beats followed by a short beat
- often uses call and response
- simple harmony
- verse and chorus songs
- topical, witty lyrics - often satirical
Here is a sample Calypso rhythm:

I have no special knowledge about calypso, but I think the list above is nice on concise and matches nicely with my perception as a casual listener.
One other suggestion: try finding folk song books in the library and browse for those in a calypso style. You might be able to find a folk song book devoted to calypso. The 1950's and 1960's in America showed a lot of interest in the general public, Harry Belafonte's first record was released in the early 50's. A lot of these folk song were published shortly after in the 1960's, maybe the 1970's too. I think these could be valuable resources for you.