CBEffects is a comprehensive, open-source, multi-file particle system package for Corona SDK. It is extremely flexible, easy to use, and completely free. CBEffects is a single library, so just copy it into your project folder and it's ready to go!
Note: I am aware that Corona has officially supported Particle Designer. Fear not! Nothing has changed with CBEffects. CBEffects remains the flexible, free, easy to use engine it always has been, and will continue in development.