This is in the same vein as taking the yellow out of teeth.
- Create a Hue/Saturation layer via Layer > New Adjustment Layer > Hue/Saturation Layer.
- Select the white box (the mask icon) of the new Hue/Saturation layer in the Layers palette and fill that with black (Edit > Fill...)
- Using the brush tool, paint white over the red in the eyes you’d like to remove.Nothing will change as we’ve not adjusted the Hue/Saturation yet.
- Back on the Adjustment Layer panel, change the colors affected from “Master” to “Reds”. Reduce the Saturation level to about 15% and raise the lightness to remove shadow in the eyes.