I don't think an old CD player can be made to play through your car's speakers. Your car radio is set up for digital computer inputs, not the old analog signals that the old CD player is producing.
An idea for a workaround. Sounds like you have a Sony CD player with no speakers. Buy some external computer speakers and hook them up to the player so you can play your music
Another idea, but it is just a guess. Look for a Bluetooth capable portable CD player. The Bluetooth connection should communicate with your car's audio system. Might be a good challenge for an auto audio store.
You can also buy an old boom box at the thrift store and make it your travelling companion.