I'm a Jamaican living in Japan. I would like to visit Beijing for tourism purpose.

You need to prepare those documents first: your passport and copy of its data page, the filled-out application form attached with a passport-style photo, your valid entry permit for Japan, and proof of transportation and accommodation arrangements.
And then submit the application to the embassy of PRC to apply for the L type.
Usually, a tourist L type may cost 4,000 yen per person.