I'm not familiar with the chip, but I also just purchased the same (well, I assume that the color and white versions are the same) light set from Kmart, oddly enough) that uses the same chip (P9816). I spent a few hours searching to no avail, and trying to modify the existing adafruit library. At last, I finally found that someone posted Arduino code (not a library, but still useful) for a similar chip, P9813, at: http://seeedstudio.com/wiki/index.php?title=Twig_-_Chainable_RGB_LED
. I was able to use this code without much modification to control my set (the set I bought has 108 leds, in groups of 9 in red, blue, green, & yellow). My modified code is at: https://gist.github.com/4006360
Hopefully this is of some use to you.
Update - I created a simple bash script that can be executed to demonstrate the serial functionality (it goes through group color assignments): https://gist.github.com/4009063