I did not use an Arduino Ethernet, but I recently used a close configuration.
I pluged a Ethernet shield and a Gameduino shied on an Arduino Mega 1280, and both shields work very fine together.
I assume that in your and my case, the SPI bus handling is the same.
The SPI bus is shared by the Ethernet W5100 chip, the SD card chip and the Gameduino chip.
Your application has just to handle their selection when needed through different CS (chip select) pins:
#define ETHERNETSHIELD_SDCARD_CS 4 // CS of the SD card chip
#define ETHERNETSHIELD_W5100_CS 10 // CS of the Wiznet W5100 ethernet chip
#define GAMEDUINO_CS 9 // CS of the Gameduino chip
The CS enabling or disabling is already handled by the Gameduino library, but doesn't seem handled by the Arduino Ethernet library (I did not have time to check directly in the library)
In my case I had to enable the Gameduino CS before the Ethernet connection and to disable it after the Ethernet disconnection.
Here is the simple code sample to select the Ethernet chip:
digitalWrite(ETHERNETSHIELD_W5100_CS, LOW); // select the Wiznet W5100 ethernet chip
For non Arduino Ethernet users, the Ethernet shield using the ICSP header, it must be the bottom shield
in the Arduino shield stack
For Arduino Mega 1280 users, the SPI connection is specific
: See http://answers.gameduino.com/question/46/mega-2560-compatibility
I hope this could help you.