If you're interested in the Peking University Law School LLM, some of the scholarship opportunities offered by the school, and some that I've pursued successfully, might be of interest to you. 

First, there is the merit scholarship offered by the school.  This merit scholarship is a cash gift of RMB8,000 that is given to five students that are selected by the Peking University Law School based on application credentials. Based on my experience, it seems that previous related work experience, publications, and academic credentials are considered by the school in selecting the recipients of this merit scholarship.

Second, there is the scholarship offered by the Beijing City Government. This is a cash gift of RMB30,000 that may be applied for by three students in the full-time LLM program who are nominated by the law school. The law school has nominated those who are able to obtain the top three grades based on the first semester of studies.

What if you got the RMB8,000 PKU merit scholarship AND obtain one of the top grades in class -- does this mean you will get the Beijing Govt scholarship of RMB30K in addition to the RMB8K? Unfortunately not! The school will no longer give you the RMB8K scholarship if you obtain one of the top three grades, and will nominate you instead for the RMB 30K scholarship.

The last scholarship that I was able to avail of are the fellowships offered by various institutions that require the submission of project proposals for studies on Chinese Law such as that of the Chinese Journal of International Law, and fellowships offered by law firms that require student applicants to compete on the basis of academic and professional credentials, as well as writing samples. Jones Day offers this for students in Beijing. 

I'm sure there are other opportunities available, but these are the ones I've explored. Good luck with funding your Peking University LLM in China! 

Chinese law profs in Peking University have classmates in Beijing law firms and could have consulted for the firms, or might even be working in the firms as of counsel. Looking for a target firm then talking to a professor about how to get an internship there, and asking for their help as early as possible would be a good way to secure an internship.

It is actually possible to do an internship search on one's own and thru one's own connections too. Using my connections, I was able to secure an internship in a large Chinese law firm in Shanghai. However, because of difficulties in processing my residence permit, I decided to just do my internship in the Secretariat in UNHQ. 

Good luck with the internship search in China! Some of my classmates have been able to combine internships with classes, and found them to be great experiences. I myself chose not to do so, because I pursued fellowship opportunities instead.