If the pulley is moving side to side then it might be the snout bearing. If there is play while rotating then its the coupler. It is easy to replace the coupler by draining the snout and removing the bolts. If the supercharger is on the bench, replacing the coupler is a 20 minute job. If there is play it will only get worse. I would replace it now.
" THE BLACK PARALYZER" -87GT 3800SC Series III engine, custom ZZP /Frozen Boost Intercooler setup, 3.4" Pulley, Northstar TB, LS1 MAF, 3" Flotech Afterburner Exhaust, Autolite 104's, MSD wires, Custom CAI, 4T65eHD w. custom axles, HP Tuners VCM Suite.
87GT - ALL OUT 3.4L Turbocharged engine, Garrett Hybrid Turbo, MSD ign., modified TH125H
" ON THE LOOSE WITHOUT THE JUICE "