Here you can find a statistical CCG parser "StatOpenCCG" developed with Tejaswini Deoskar.
StatOpenCCG is trainable on CCGbank and implements several generative probabilistic models based on the work of Julia Hockenmaier and the code is based on the OpenCCG platform developed by Jason Baldridge and Michael White. You can find a description of the model and some other aspects of the parser in my MSc thesis.
It was designed mostly for readability and ease of expansion rather than performance---optionally it can perform unification check to allow only strictly CCG-legal contructions.
We have also implemented a semi-supervised version of the parser which performs EM to re-estimate its statistical model from unlabeled data. If you want to use this version please email me.
The main package also contains a graphical version of the parser which illustrates the use of the API.