AC90 pilot reports deviating around weather without clearance when frequency congestion prevents requesting a deviation in a timely manor. The Controller is apparently understanding and the pilot lands safely at destination.

Narrative

I was flying a newly purchased Turbo Commander 840 to San Juan. Before departure; the TAF included thunderstorms in the vicinity and the San Juan radar was showing weather coming in. During my flight; I asked for and received deviations from Miami Center in various occasions. Close to GTK I was given a new route to BOCCA; which I accepted and was flying towards. After switching to San Juan Center; I started my descent from FL250 and immediately started penetrating weather and light turbulence. My radar was not painting much. The frequency was busy with various flights. While in my descent a pilot flying a Baron informed San Juan Center that he was running into weather and asked for deviations. He had to make repeated requests and the Controller seemed reluctant to offer a deviation. I continued my descent passing various layers with light turbulence and it seemed to me conditions were deteriorating as I approached San Juan. Turbulence was increasing. One pilot asked for a deviation and was told to standby; by another voice. It appeared that we were under a Controller change. As I had been flying the same heading for some time; I felt that either the weather was fine or I was not being vectored around weather. I don't recall the exact altitude; but somewhere between 10;000 FT and 6;000 FT I broke clear and saw before me a towering cumulus; turning into a nimbus. It was painting red in my airborne radar. I had been flying the same heading since descent. The Controllers were busy with a change; the frequency was saturated. I waited until the last moment; then I decided to turn around and I started to circumnavigate the weather to the east as best I could while continuing my descent. I have TAS and there were no aircraft close to me at that point. I continued my descent and the Controller got to me. He questioned my position and altitude; I informed him politely that they were busy and I was avoiding a thunderstorm. I continued with him experiencing downdraft's and light turbulence. I punched out of the weather and continued a normal approach to San Juan. I am writing this to explain my decision and ask that a NEXRAD antenna be installed in San Juan. I have experienced NEXRAD weather in the U.S. and this technology would greatly benefit all Caribbean flyers. [Satellite weather providers] do not plan to cover the Caribbean in the near future.