I entertained the idea of using a small portable CD player in my Wrangler, too, but a small USB drive filled with music ripped from CDs works a lot better. You can use the onboard display to navigate the contents of the USB drive by album or artist.
I use Windows Media Player to rip music from CDs to the USB thumb drive. The only bothersome hang-up is sometimes the first track of the CD doesn't get the right album and artist info, so I have to manually fix it by going into the Properties for the file.
Best option is to rip/burn your CDs to, at minimum, MP3 format and then copy the files to a USB drive. There are other formats that can be used for higher quality.
A portable USB CD player may not actually work with the USB ports in the JL. If you insist on CDs, you might just want to use a regular portable CD player and connect to the AUX jack.
Yeah, I ripped my whole library to mp3 or better. I’m not that audiophile savvy. I did save some special CD’s but there’s no need to actually play them since everything can fit on thumb drives and take up a lot less space. I’d highly recommend that route.