which brand of cd player supports re-writable discs?

i need to know becos i want to burn some mp3 on a cd-rw so i can transfer the songs onto a cassette tape and reuse the cd-rw for more burning.

i have an old magnavox portable system that always says "no disk" when i try to play a cd-rw with burned music on it.

id like to know which players with dual cassette (or single, preferably dual) recording and cd-rom capabilities support the rewritable disc.