A thick cloth wall hanging might be helpful, or some insulated drapes. You could even use some carpeting.

I meant something of a more permanent nature like adding drywall over the block wall but I'm not sure what I should use between the wall and drywall to sound proof it.

Just a thought.... What about using ridgid insulatione between the wall and drywall? You'd have to frame out some, but you'd have to do that to hang the drywall anyway.

Like I said, just a thought.

They make insulation that is more sound proofing than other insulations. The only way I can see you doing this thou, is if you build a stud wall the whole length and height of block wall and fill it with the insulation.

R-11 insulation is used between walls to help when sound proofing. Remember, where ever air can pass from one area to the next, sound will too. So make sure the wall is sealed up tight. Electrical outlets commonly allow air infiltration so make sure to sound proof them.
Once you put in your drywall over your insulation, use chalking or "soft" spray foam to seal up the gap between the rock and the floor. I read a little about sound proofing in a HandyMan magazine once, so that is the level of my expertise.

Drak