Radiesse for Under Eye Bags?

A good exam by a Board Certified Plastic Surgeon would be the best place to start. The question is what exactly is the anatomic issue that is causing the aged or "tired" look of your lower eyelids: is it too much skin, bulging fat, a deep tear trough, or a combination of these factors? Once the problem is properly identified, then you will have some options.
If indeed it is simply the tear troughs being too deep, I would personally recommend Restylane for this area, not Radiesse, Perlane, or Juvederm. Radiesse and Perlane are both simply too thick in my opinion for injection into such a delicate area, and the risk of both significant swelling, bruising or obivous bumps after the procedure can be high.
Juvederm, while similar to Restylane, is more hydrophilic (attracts more water) which makes it a great options in areas that you want to be more plump (like lips) but not as good under the eyes, as it can cause significant swelling that can take months to settle.
Some other surgeons may have a different experience with these products, and so I think it is important to have a good exam and consultation first before deciding on the course of action that would work best for you.
Dr. S

Radiesse is actually an excellent choice for the under eye area, provided that it is being used skillfully by an experienced practitioner. The reason is that it is a white colored substance that offers the appropriate level of support to help reshape or reposition mild to moderate bags so that they don’t protrude. Also the coloration of Radiesse helps it to camouflage darkness beneath the eyes as well. The risk with hyaluronic acid fillers is that it is a clear gel which is subject to a light bending phenomenon known as the Tyndall effect, resulting in bluish hue.You can see a patient example of Radiesse used in the under eye area by clicking the link below.

It is not recommended to place Radiesse at the under eye area. This is a thick product and is white in color, so it can cause visible and palpable lumpiness and is much more visible due to the thinness of the skin underneath the eye. There are other products such as Juvederm or Restylane that work well for the under eye area, but must be injected by a skilled practitioner as this is considered an off-label treatment.