Assuming your player is compatible with what you're planning, I would make a 'silent' audio CD this way:
(a) Open a digital sound editing program. (Example, Audacity is free, and popular.)
(b) Generate several minutes of silence in L & R channels. 70-75 minutes is a reasonable maximum that will fit on an audio CD.
(c) Save as '.wav' file.
(d) Burn the wav file to CD. Your Mac and Windows OS can do this directly, if it's a recent version.
Not all CD's will be recognized in all players. The most reliable scenario is a CD-R, plain color.
Not so reliable is a CD-RW, or blue tinted.