We loved Zak, the beijing taxi/private driver, with a small convenient black car.
Call him direct at 00-86-131-611-39637. negotiate wth him and be fair. he is perennially available and will pick you up or drop you anywhere in beijing and anytime. FYI, for private drivers, to/from airport to central Beijing is 200RMB ($35). It is absolutely necessary to have someone available in beijing, as the taxi situation is miserable! You will need one like Zak, and he has ok converssational English.