Sampan Pidgin - being a history of the Shanghai Rowing Club, N M W Harris
Published in 1938 by a keen rower and rugby player. This is one of only two books that I have found which focus on the history of a single sport in Shanghai. For more details see here

Rowing

China Races, Austin Coates

Many people know that horse racing in Hong Kong was and still is a major event in that city. Some may know that the Shanghai Races were also a highlight of the sporting calendar before 1941. The real surprise with this book is discovering the numerous other places in China where racecourses were built and races run.

Hunting Opium and other Scents, Maurice Springfield

Published in 1966, this short memoir of Springfield's life includes some lovely stories from his time in Shanghai from 1905 to 1933 serving with the Shanghai Municipal Police. 

A History of the Shanghai Paper Hunt Club 1863 - 1930, C Noel Davis

Published in 1930 with an addendum in 1938(?), it includes lists of all races and winners, numerous photos and cartoons drawn by Edmund Toeg.

China Sports

The History of Sport Played in China's Treaty Ports

The Little Red Book of Chinese Football, Dave Twydell

This 1994 book covers a lot of ground and does a good job of digging out information across China. The sections on Shanghai are interesting but include quite a few errors. The first 'true' football club according to this book was established in 1887. This is actually twenty years after the first club was established in 1867. Despite the errors an interesting read.

Life and Sport in China, Oliver George Ready

Originally published in 1904 and now available as a reprint, the sport in this book is primarily concerned with guns and horses. It provides a good snapshot of the life of a gentleman in 19th century China and how sport was as, if not more important than work.

Horses

Football