I am not eligible for a CSC scholarship and therefore cannot apply for the FUB - CSC PhD Program. Are there other possibilities for funding PhD studies at Freie Universität?
In terms of the number of availabe scholarships, the CSC's programs are certainly your best option. But there are some alternatives: The DAAD - German Academic Exchange Service - is offering scholarships for doing a doctorate in Germany, too. Check the details on the DAAD Beijing Office's homepage.
Some of the structured doctoral programs and research training groups of Freie Universität Berlin have their own scholarship programs. These scholarships are given away on a competitive basis. Calls for applications are open to German as well as international applicants. Calls are published yearly, in the case of some programs only every 2 to 3 years. For information about these scholarship opportunities, see the homepages of the individual programs. A suitable starting point is the List of Graduate Schools and Research Training Groups at Freie Universität Berlin.
Finally, in some cases, the German supervisor could be able to cover your living expenses from his own third-party funding.