It's a great photo of Fluffy, except for one little problem. The light was at just the wrong angle when you were taking the photo, and your beloved pet ended up looking positively demonic, glowing eyes and all. No need to call an exorcist -- like red eyes in humans, yellow or green eyes in animals can be easily removed in Photoshop by painting over them.
Open your photo in Photoshop and examine it, looking for a dark area that is a nearly black color. In most cases, areas that look black in a photo are dark gray, and true black exists nowhere in the photo. This means if you paint over the eyes using a true black color, the result is unrealistic, because the black sticks out like a sore thumb.
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Press "I" to switch to the eyedropper tool. Click and hold over the dark area you identified and then drag the tool around, watching the color change in the top half of the sampling ring. When the color switches to a suitable dark gray, release the mouse button to set it as the foreground color.
Click the "New Layer" button in the Layers pane to create a new, blank layer.
Press "B" to select the Brush tool and then press "F5" to display the Brush pane, if it is not already visible. Select the "Hard Round 30" brush preset.
Move the cursor over the eye, and compare the size of the brush tip to the size of the area you need to paint over -- the goal is to cover the entire glowing pupil with one single click. If the brush tip is too small or too large, position the cursor so its center is roughly where the center of the eye is, hold "Alt," right-click and hold the mouse button. Drag to the left to decrease the size of the brush tip and to the right to increase it. A red circle shows the exact area covered by the brush tip. When you're satisfied, release the mouse button and then release the "Alt" key. Remember to account for the entirety of the pupil, not just the visible part -- if the animal's eyes are half-closed or it's looking up, part of the eyes may be obscured. If the animal has round pupils, skip the next step.
Change the brush angle in the Brush pane to 90 degrees. Set the roundness value to 50 and compare the brush tip to the pupil again. If the width of the brush is too narrow, adjust the roundness value up; if too wide, adjust it down. Ultimately, this is a matter of trial and error. If you're unsure whether the value you've selected will cover the entire pupil in one click, test it, pressing "Ctrl-Z" to undo afterward.
Click once over each pupil, painting the dark gray color on the previously blank layer and covering the glowing eye. Unless the animal's eyes were perfectly round and wide open, the dark gray will stray outside of the eye and cover some parts of the animal's face. If you are certain this is not the case, skip the next three steps.
Click the "Add Layer Mask" button in the Layers pane. This creates a mask that can be used to selectively hide or reveal the contents of the layer; by default, the mask is completely white and the contents of the layer are fully visible. When you create the mask, it becomes active; the foreground color changes to black and the background color changes to white.
Set the brush roundness in the Brush pane back to 100. Adjust the size of the brush until the arc of the tip matches the arc of the animal's eyelid. Positioning the brush carefully to cover only the area where you know the glowing pupil is, paint with black on the layer mask, clicking once over each eye. This hides the parts of the layer that are over the glowing pupil -- the opposite of what you want.
Press "Ctrl-I" to invert the layer mask. This turns black areas to white and vice versa -- hiding every part of the layer except for the area over the pupils. If at this point any part of the glowing pupils is still visible, press "Ctrl" and "+" to zoom in, reduce the size of the brush tip, press "X" to switch your foreground color to white and carefully paint over the mask in those areas to reveal the layer, hiding the glow.
Create another blank new layer and examine the image to determine where the light is coming from. Set the foreground color to white and adjust the size of your brush tip until it's small enough to add a realistic bright glint to each eye -- the exact size will vary depending on the size of your picture. Click once on each eye to add the glint.