Suggestions on used CD Player with Volume Control

AH! Njoe Tjoeb 4000 or Cary 303/300. Don't use the stock tubes, though. Recommend Ediswan CV-2492 for the Tjoeb, and RCA 12BH7a for the Cary.

Levinson No.39 or 390s but will cost a little over 2k. Another option would be a Linn Genki.
Good luck!

I love my Shanling CDT 100, well below $2000, 2nd hand and some money to spare for modding later if you wish

Cary 308 (solid state) or 308T (tube output), both are very good and fit within your budget figure.
Regards,

Keep an eye out for a used Wadia 830. They sell quickly but they're usually around $1800 or so. If you could stretch to about $2500 you might find a used Resolution Audio Opus 21, an excellent player. Also there are occasionally older Accuphase players for around $2K, like the DP-70 or DP-65, not the V versions. Also search the archives as this question has been asked hundreds of times.