Can I apply for tourist visa in Beijing when I'm on business visa in Jan-May 2012?

I'll be studying abroad in Beijing January-May 2012, then leaving China, then coming back as a tourist in June. Will it be possible, while on my business visa in January-May 2012 and in Beijing, to apply for a tourist visa that will allow me to enter the country in June? Where do I go to apply for a tourist visa in Beijing? And how long does it take?