You could either multiplex (this I have tried and know it works) the chip-select (CS) line of the SPI, for communicating with them alternately, or you could dedicate a second digital output as a second chip-select for activating your other device while halting the communication with your Ethernet shield. (this should work, but I haven't tested it.)
Communicate with one while halting an other would mean I could only use half the speed of spi for each device. I need a very high speed for my led spi controller.
Is there any other solution ? Maybe with 2 arduinos ?
Is there a non-spi way to communicate between 2 arduinos ?
I found that adafruit library can be set in a "soft spi" mode. So it leaves the "hard spi" pins available for ethernet shield.
Soft spi is of course not as fast as hard spi but it might be enough for many applications.
I'll try the I2C trick with 2 arduinos if the soft spi isn't fast enough.