1. Use CD-R disks not CD-RW disks.
2. Burn in Audio format & not mp3 or data format.
3. Burn at a lower speed. Some CD players don't like disks burnt at maximum or high speeds. Not too many years ago, if you burnt an audio disk at faster than single speed you couldn't play it on CD players. So the concept is a little similar, just be careful not to choose too high a burn speed.

BTW DVD players are less fussy than CD players. They can read CD-RW & also should be able to play mp3 disks depending on your particular player.