I don't think any portables use a true digital volume control, and if they did, i don't think it would be a good thing.
I think most CDPs use digitally controlled step attenuators, which connect different combinations of resistors into the signal path to decrease the volume.
In theory, this is a great idea, because it should be able to provide much better performance than a pot (especially at that price range). Also, when used with a remote control, the volume can be adjusted via a digital interface, rather than having to add a second cheep pot into the signal path. But in actual practice, they must use very inferior parts and designs because most newer cdps that use them are somewhat noisy and have poor dynamics.
A true digital volume control is rarely used, except in computer soundcards. These actually use mathematical algorithms to reduce the amplitue of the samples, before they pass to the DAC. So at full volume, you will have a perfect signal with full resolution (and no analog pot in the signal path), but as you decrease the volume, the resolution will decrease greatly. So if you listen at low volumes, the resolution may be 8 bits or even less... So there will be an audiable degeation in the sound with true digital volume controls.
I think the newest Sony MDs allow you to select between line-level output and amplified headphone output digitally. Supposedly, there is quite a large difference in sound between the two, even though they use the same jack....