AIM 4-4-10 (d)
Climb or Descend at a rate consistent with the operating characteristics of the aircraft to 1000' above/below the assigned ALT. Then maintain 500-1500 fpm to the assigned ALT.
Advise ATC if you cannot maintain at least 500 fpm.
That should be the answer, unless the AIM contradicts itself somewhere else.
However...if you descend at 500 fpm out of the flight levels, expect ATC to get upset (unless you doing a crossing restriction). They plan descents based on what most airplanes usually do (2000-3000 fpm), not 500 fpm.