Chinese Visa after divorced

I married over 6 years, got 4 times 'L visa', and latest two where 'Residence Permit' (family visa). Now, we are planning to divorce, but we have a 3-years old baby, and I obviously I want to stay in China with her for years to come.

Can a foreign spouse divorced from a Chinese national get Residence Permit, or any kind of visa for that matter, to keep in China to visit relatives (my daughter). Technically my daghter still my relative, and despite divorced, I still her father (I appear as her father in her Chinese birth certificate).