Check out
http://www.realoem.com/bmw/showparts...19&hg=51&fg=30
It looks like you need to take off #3 and then remove the fillister screws (#4). From there you can prob just pull out the whole cup holder and try to reseat the spring. I was messing around with my rear ashtray a few days ago and the mechanism looks similar. There was a small round plug on the bottom that prevented the whole tray from coming out. If I am right you need to remove this plug before you can take the cup holder tray out to access the springs. Good luck.