Did a fresh install and only installed CSD. The fresh install seemed to have been unnecessary. I discovered that CSD doesn't let you make peace immediately, which explains why I thought it was broken before. The Diplomacy menu works fine without the EUI. With the EUI I still could not get the Diplomacy menu to come up. For fun, I tried deleting DiploList.lua from the CSD folder, and then the diplomacy comes up fine. I hope that doesn't accidentally hide other features?
I did notice another interesting bug when testing (or maybe just another feature). While at war with a CS, it is impossible to meet any other CS. You will go into their territory but won't get gold or see a screen pop up. Once you make peace, you will instantly meet all the CS that you met while at war with another CS.