Broken Supercharger?
 

I recently completed my supercharger build and have noticed that at idle/cold start it will make a fairly loud knocking sound. The pulley is dented on the top and it looks like someone dropped it in the past. The supercharger has amount 1 cm of play either way but turns smooth after that. After searching online I found it may be the coupler but I'm not sure. Any advice on how I should deal with the problem?
attached is a non helpful photo.

replace the coupler, you will need to replace the oil as well.

If it was me, I would replace the snout bearings ...

HOLY MOLY 1 cm of play, and you installed and ran it? lol

I think 1 cm was an overstatement, probably a few mm of play, enough to wiggle it back a forth and hear a little click.

So what all did you replace?

I would have that looked at. There should be no play. When was the last time the bearings or oil was serviced? I had a lockup on my MP62 because I did not check those things.

Rebuild the snout. Fairly easy and there are kits available to get rid of that cement mixer noise.

As little play as there should be, I had a noise similar to how you described it with mine, it turned out to be the tensioner pulley, one had failed and the aluminum pulley was slipping on the steel bearing outer race.