I know I'm no expert, but won't a CPL take care of most reflections from glasses?
That depends on the reflective qualities of the glass...and even if there is Polarized Direct Reflection, it will never be more than 50% of the total direct reflection. So no, you can't get rid of it with a polarizer.
Is there some way to keep them from reflecting?
The reflection you see on the glasses is a direct reflection of the light source. Imagine that the glasses are a mirror, and if you are looking at them (from the angle of the camera), if you could see your light source in those mirrors...then the light source is in the 'family of angles' of the glasses, and thus you will see the direct reflection.
The key to getting rid of the reflection is to move the lights outside of the 'family of angles'. In other words, move your lights (or change the position/pose of the person) so that there are no light sources where they will be reflected by the glasses.
For example, if you are lighting your subject with 'short lighting', then you are much more likely to encounter reflection on the glasses. But if you use 'broad lighting' on them, the light won't be in a position to reflect in the glasses. Of course, there are other reasons why you would choose to use short or broad lighting...so all things must be considered.
A rather simple solution that often gets over looked, is to remove the lenses from the frames. It only takes a few minutes with the proper tool and it will fully solve the problem, not to mention the problem of distortion seen though the glasses.
Also, if that person is directly facing the camera, or close to it. Or if their hair style will allow. You can try lifting the arms of the glasses, so that the lenses tilt downwards a little bit. If you can tilt them enough to get rid of the reflection, without making it noticeable, then you have a solution.