Don't start packing up your passport in a Fedex envelope to send back to the States, because you can apply for a visa to a third-party country while residing in a foreign country. The Chinese embassy will issue foreigners in Japan a tourist visa as long as they follow the proper application channels. The application form is slightly different than that for a Japanese citizen, and the fee increases five-fold. In such cases, an appointment is not necessary. Walking in to your nearest Chinese embassy or consulate is your surest bet at securing a Chinese visa.

Chinese Consulate

Locate your nearest Chinese Consulate General. There are five Chinese consulates in Japan; in Fukuoka, Nagasaki, Nagoya, Osaka and Sapporo. The Chinese Embassy of Japan is located in Tokyo. Based on your location, choose the consulate or embassy that is most convenient for you to access. For many Americans used to rigid consular appointment rules, walking into a consular office without an appointment may seem a bit daunting. However, you will need to go in-person and state your situation. Visit the consulate during office hours (9:00 -- 12:00 Monday through Friday). You will most likely be directed by an officer to the visa department, after which a visa agent will likely provide you with the proper paperwork, which will be different from what a Japanese citizen would fill out.

Application and Fee

Complete the application form and return it with two passport-size photos and your passport. If upon request of the application you were asked to provide other supplementary information such as proof of your residency in Japan or proof of Japanese visa, make sure to do so. You will need to leave your passport at the consulate until your visa has been granted. When you submit your application, you must pay the processing fee; for Americans in Japan the fee is 15,000 yen for all forms of L visas. The processing time should take about four days, after which you will be instructed to return to the consulate to retrieve your passport and visa.

Japanese Re-Entry Permit

Before you leave for China, make sure you apply for a re-entry permit to get back into Japan. To do so, download the application form from the website of the Japanese Immigration Bureau (link found in References below). The link is found under the bullet "Entry Procedures" and "List of Necessary Documents." Choose link six, "Application for Re-entry." You will need to submit it, along with your passport and proof of legal Japanese residency (or visa) to the nearest Immigration office. You should be issued the permit on the same day of application.

Source:

Travel China Guide: Embassy of the People's Republic of China in Japan

Japanese Immigration Bureau: Re-Entry Permit

More Information:

Japanese Immigration Bureau: Immigration Procedures Guidebook