I've got an Adafruit 1.8" LCD/SD screen that works fine with my 2560. I just got an Ethernet shield that also has an SD card on it.
The instructions for the Ethernet board says it uses SPI connections which is also what the LCD uses. Is there no way to have multiple devices connect to the SPI?
http://www.robotshop.com/content/PDF/datasheet-a000031.pdf - Ethernet datasheet http://www.ladyada.net/products/18tftbreakout/ - LCD screen.