Using SPI with an SD card and a TLC5940 Led driver

My current project involves attempting to use both an SD card and a TLC5940 Led driver, which both communicate using SPI.

As I understand it, the SPI master device ( the Arduino ) controls a separate chip select line for each slave device, and pulls that line low for the device that it currently wants to communicate with.

The SD card module has a chip select line and that scheme works just fine. But the TLC5940 doesn't. What is the best way to prevent the TLC5940 from corrupting it's data when it attempts to read SPI signals which are actually being sent from the Arduino to the SD card ?