cdrw's generally have less light reflection than cd-r's, and cdr's have less reflection than stamped cd's. Many older players have trouble reading cd-rs, let alone cdrw's. If it can be read with cdr, then thats great use those, there only what $0.05 a pop nowadays. If you need cdrw's you could try a different brand name. Im not sure what is the best to try.
if its an older player, maybe the lense needs cleaning. Which I personally have never done, so my knowledge stops there.