The C backend was dropped in release 3.1 because it was not maintained and started developing code rot, becoming a burden. Since no maintainer stepped up, it was removed from the tree. From the release notes of 3.1:
The C backend has been removed. It had numerous problems, to the point of not being able to compile any nontrivial program.
In August 2012 a thread on llvmdev discussed reviving the C backend, but I don't think it ended up anywhere useful.
You can still download LLVM version 3.0 (from the releases page), build it and see the C backend in action, study its code, etc. For your specific purpose - looking at the code and figuring out how it works, the 3.0 C backend should be good enough.