No tray needed, there should be some kind of braket holding the drive in place. If you open your laptop drive cover, you will see how it is held in place. All you do is remove the braket (or whatever is holding it) and use the same one on your SSD.
Its very easy, should only take a few minutes. I have done it on my work laptop with a 1.8" drive, there was absolutely no problem fitting it.
Besides, I'm sure Sony sells the same model with an SSD option.