Here's a nice little calypso tune written by Cyril Neville. The recording is pretty straightforward: Melody, Trombone Solo, Melody, End. Even though it has a simple form and harmonic structure, it's what these musicians say and how they play "within the boundaries" that make this tune so much fun.
The melody uses both short syncopated rhythms and long tones in the span of sixteen bars. This is a great exercise in developing your air support. While you will need the constant stream of air for the long tones, you will want to keep that air support during short rhythms, as well. Instead of inhaling during the rests, think of the shorter rhythms as one long continuous phrase, and simply use your tongue to break the air stream and create the silences.
The solo should also be thought of as four long phrases. The first phrase is simply playing around with the original melody by using syncopation. The second phrase embellishes these melodic ideas, but returns back to the original rhythmic feel (those D's should be played out in the alternate forth position, by the way). The solo climaxes in the third phrase by jumping up to the high G, and then slowly walks down the scale. It arrives back at the tonic G by the forth phrase, and plays around once more with the original theme. Make sense? Have fun with it.
I couldn't find one for this tune, but here's a YouTube video of Trombone Shorty playing "Summertime" with Cyril Neville. Shorty actually plays the trumpet during his solo, and it should be noted how his trumpet phrasing carries over to the trombone.
Recommended reading: Truth in Comedy: The Manual of Improvisation By Charna Halpern, Del Close, and Kim "Howard" Johnson. Published by Meriwether Publishing Ltd.