To clarify:
Your emergency should qualify you for a landing visa. To apply, you need to present a prof (a notice of your father's critical illness from the relevant hospital), along with your birth certificate, passport and a recent photo. Landing visa services areas, which run 24 hours a day, are in the arrival halls of terminal two (6459-0454) and three (terminal 6453-2939) at Beijing Capital International Airport. Applicants can visit xxx.gov.cn/eng/ and download the necessary forms in advance. Visiting a sick relative is just one of the qualifications for applying to get a landing visa, however. The others are:
people invited at short notice by a Chinese company to attend a trade fair;
people invited to enter a bid or to formally sign an economic and trade contract;
people coming under contract for supervision over export shipments, import commodity inspections or to check on the completion of a contract;
people invited to install equipment or make urgent repairs;
people coming at the request of a Chinese body for settling claims;
people invited for scientific or technological consulting services;
a last-minute replacement or addition, approved by a Chinese body, to a delegation or group that has been invited and has already obtained visas;
people making funeral arrangements for foreigners who die on Chinese soil;
people in immediate transit who, because of force majeure, are unable to leave on the original aircraft within 24 hours or by other means of transport;
people who don't have enough time to apply for visas to Chinese agencies abroad but hold letters or telegrams from the designated competent authorities approving their application at port visa agencies;
tour groups organized and received by international travel agencies on the Chinese mainland or approved Hong Kong and Macao agencies.
To use the landing visa service, all applicants must produce a visa application form, a recent photograph - 5 centimeters is size - that shows the full face on pale blue background, a valid passport and the relevant papers to support the application, such as:
a letter or telegram from an organization authorized by China's Ministry of Foreign Affairs for an F visa;
documents concerning an emergency for an L visa;
a certificate of reception from a Chinese mainland international travel service or an approved Hong Kong or Macao agency and a list of the tour group for an L group visas;
a valid visa for entering the country (region) of destination and a connecting ticket (air, train or boat) for G visas;
an official letter from China civil aviation department or transportation administration for C visas.