Which multiplicatively homomorphic encryption scheme supports encryption of 0? I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). 

I also want the multiplication to be operated on the ciphertext of 0, i.e., if one of the ciphertexts is encryption of zero, the product is also encryption of 0.
Gentry's recent work highlights both FHE and SHE with and without bootstrapping easily found on Google Scholar. The open source code on Github is getting closer to reducing the associated complexity. IMB and Microsoft have a myriad of code and papers on the subject.

Having said that what you are proposing has never been done before, but here is one helpful papers that may assist you depending on your commitment:

http://eprint.iacr.org/2011/607.pdf

It does not solve your issue but it does present some helpful side points that may assist you if you read it enough.