Using an Ethernet Shield and a tlc5940 together
When using multiple SPI devices the normal way to have them share a bus is to assign them distinct slave select lines. The problem here is that although the '5940 libraries use SPI to send data to it, the '5940 is not actually a proper SPI device and so lacks any sort of slave select line.

All is not lost, however. Since the '5940 responds only to SCLK (and GSCLK of course, but you should be running that one separately) all you need to do is inhibit it while nSS for the Ethernet module is active. This can be done with just a little bit of external circuitry. Since nSS must be high in order for the Ethernet module to be inactive, we can AND SCK with nSS to derive SCLK from it.

Using a 74HC08 for this would work, although it leaves 3 of the gates unused. A 74HC02 will let you do it with no wasted gates, but with a slightly higher propagation delay.

And of course, the requirement to clock in the grayscale data before the grayscale cycle completes is still there; properly interleaving this with the Ethernet communications is left as an exercise for the reader.