We r currently remodeling a concrete block room that sits on a slab.  It was built in the 1950s and we have had moisture problems in the past.  So we want to be sure we know what we are doing now.  When we took off the drywall the blocks look like they were painted with something black.  Now i have bought the pink polysterene insulation.  Is that the correct way to go .??  What is the black stuff they painted with.  Tomorrow is the day they are gonna be working on this and we r a bit worried about this.  Any suggestions.?

The black is most likely a tar based waterproofing coating. You should inspect this coating carefully before adding the coverings back to the wall. Look for cracking and/or signs of water penetrating the walls. Depending on the particular type of product used, this coating can be very thin, like paint, or up to 1/8 inch thick. The thicker product is more likely to have dryed and cracked. If it is the thin, paint like, product and it is in good condition, then you mike think about adding a new coat of waterproofing, such as Drylok, before closing the wall again. If the product is the thicker product and is in good condition, you should be OK. However, if the coating is cracking, or if you see signs of significant water leakage, consult with a waterproofing professional before recovering the wall. Otherwise your work may have to come back off in the future for the repairs that should be done now.

Will the block be left exposed on the outside?

yes it is exposed on the outside.  The coating almost feels rubber like.

Since concrete block is so porous, it is noramlly damp proofed from the outside and then covered with some type of facade.

renaslayton,
The black tar coating is on the inside, correct?
Are these basement walls or above grade?
If they are above grade, then the best solution would be to seal and insulate the outside of the blocks.
If the tar is on the inside, and below grade, then I suspect it was an afterthought, probably in response to the original leaking of the walls.

What are your plans for flooring? There are dimpled plastic panels that keep slab moisture away from the flooring. There are also moisture proof wall boards.