The release mechanism inside the SD card slot seems to be broken, so when I press the pin into the hole, nothing happens. This would have been OK if I were using the right SD card - instead of my wife's.
I had to remove the back of the iphone 4s, remove all the screws from the logic board, remove the battery, and then I was able to loosen up and shake it enough to get the tray to fall open a couple of centimetres. I then grabbed the tray with pliers and it slid right out.
iPhone screws are almost ALL different lengths and sizes. Get a way to store screws logically and visually as you remove them - otherwise you may be trying a bunch of them over and over again.