take the sc belt off. grab the pulley, and snap it back and fourth, if you feel slop thats your noise.
you can also start the car up with no sc belt, if the noise is gone, you know its the sc in some way. chances are its the coupler. make sure you get 2 bottles of GM supercharger oil, only the dealer has it or buy it on line.
and get some latex gloves, and wear 3 pairs at a time to keep the used oil off your hands, pump the old out, ( old windex bottle spray pump works well) and have some rages under the snout to catch what runs out when it comes off, also have a can of brake cleaner or 2 around to clean up the sc side and the snout side, and the mess that will drip out.
you also are supposed to use a sealant i can never remember the name of to re seal the snout to the case, i used high heat black rtv, its been there for 2 years with no leaks.
search you tube for vids if needed. lots of vids on there.