I don't think its possible to totally get rid of them. Mine are an unfortunate family trait! Here's a make-up trick: Put some eye cream under your eye and blend. Take a Red (yes, red) creamy eyeliner pencil and draw a curved line from the inner corner of the bottom of your eye through the center of your dark circles. Then take yellow concealer - Lancome makes a good one - put that over the red line and blend. It sounds crazy, but the red counter-acts the dark undertones from the under-eye circles, and the yellow counter-acts the red. If you need to, you can put regular concealer over that.
Sounds crazy, but it really works. A make-up artist showed me the trick.
I had fun with it by asking my hubby how I looked with the red lines drawn under my eyes before I blended the concealer over it the first time. The look on his face was priceless!