I entered Kunming on a 30 day double entry tourist visa last month.
I went to the PSB on Beijing Lu today and they are processing my application for a 90 day extension to my tourist visa. In case it's of interest to anyone, here's what I needed:
1. Passport (and photocopies of front page and visa page)
2. Proof of residence – 住宿证．If you're staying in a hostel/hotel, you just write that.
3. 2 inch passport photo *1
I also brought a Kunming local along with me, who is vouching for my application, and she brought along her:
1. Id card- 身份证 (and photocopy)
2. Hukou 户口 document (and photocopies) note- you need someone with a Kunming hukou
My friend was required to handwrite and sign a letter saying that she is vouching for me (template provided at PSB).
The customer service officer told me that I will be able to leave and re-enter China once (in accordance with my existing visa conditions). Regardless, my visa will expire 90 days from now. I will pick up my visa a week from today- I don't believe they provide a rush service, though I didn't ask. In Kunming, flexibility trumps efficiency, and I'll take the lack of a rush service for generous days extensions.
Hope this is useful to the international community.