Supposedly any DC's manufactured after 10/2000 won't play CDr's. But, I don't believe any that were made after the magic date were released in the US. Sega announced they were making changes to the DC right around the same time they said they wee going to discontinue it. There are two known models that definetely don't work, one is a special Hello Kitty DC, the other was some kind of sports bundle, both of which were only released in Japan.
You are able to see when it was manufactured by looking through the hole on the back of the box. If you can't find an earlier model, try looking around for used models. EB was selling new for 70 bucks, but when I went to buy they were out. They had used for 40 with two controllers and a memory card. You can also try pawn shops.