Extension of stay beyond visa-free period when in China

I hold a Singapore passport and had bought air tickets to China for a 9-day trip - flying into Xiamen and flying back from Fuzhou. It's not confirmed yet but I may need to stay for another 10 days (and thus exceed the 15-day visa-free period), can I apply for a visa then in either Xiamen or Fuzhou when it's confirmed that I need to extend another 10 days in China?