Which DAC would be better to play my cds through?

@elmer444 DCM-390 has coaxial out. Your best option is to use it to feed the external DAC then use that DAC’s RCA analog outs to drive the amp. A decent external DAC can be had used under $500. 
You can use optical from 390 into DAC as well but expect coaxial to sound better

If you are looking to use the amp’s dac then it’s a matter of priority. If you prioritize cd playback then use coax from 390 into that amp dac and use optical with blue ray 

 You’ve received some great info from some very knowledgeable people, might I suggest this. Are you currently using an entry level coax cable for your Blu-ray to receiver connection? Try an Audioquest Forrest or Cinnamon digital coax cable. Get one from Amazon that offers a 30 day return policy and try it on your CD and see. Since you’ll have to disconnect your Blu-ray , try it on both and see ( hear ) if there’s an improvement. Other than that you’re stuck at the starting line. Regards, Mike B.

Play the cd on the Blu-ray player and see how it compares to the CD player. It may surprise you. 

I’m using an older Rotel CD player with a newer Cambridge Audio CXA-81 amp which has an onboard DAC. The newer DAC in the amp generally sounds better than the 25 year old DAC in the CD player. But I have the CD player hooked up via its analog out and the digital optical (no coax on CD player). I will do an A/B between the two and on some recordings I prefer the 25 year old DAC’s sound. Maybe try that on your system.

The DAC in your amp has one optical and one coaxial. Your BluRay has only coaxial, your CD player has both digitals and analog. 
My suggestion is that you connect the BluRay to your TV with HDMI, and use the optical output of the TV in to your amp’s optical input.  Then connect the coaxial and analog outputs to your amp.  Don’t forget to configure your TV to send PCM stereo to its digital output.