LIGHTDIMS Stickers: These dark transparent stickers are manufactured exclusively for the purpose of covering up standby lights. Their products come in "dim" or "blackout" varieties and one package includes several stickers in different shapes and sizes. They're cheap enough ($5.99 plus 99¢ shipping) to solve your problem, but there are plenty of less-costly DIY routes, too.
Lithographer's Tape: A roll of translucent red Lithographer's Tape is only around $5, and you'll probably get a lifetime of LED-dimming stickers out of it. It will, however, give each of your newly-dimmed lights a slight reddish tint.
Transparencies: You know those semi-transparent binder dividers you can buy for like a buck at the office store down the street? Well if you cut one down to the size of a too-bright display, then spritz it with a bit of water, you can effectively dim bright backlights and still read through the display.
Frosted Scotch Tape: Semi-frosted office tape will do the trick to dim standby lights, too. It might not be the most polished solution, but it will be the quickest one if you find yourself with sudden insomnia at 3 a.m. Layer it on for more effectiveness.
Sharpie Markers: Color over the glass in front of the light with a black or blue permanent marker. It will still let a bit of light through, but it will dim the eye-burning brightness by quite a lot. You can also pop open your device and color directly on the LED bulb, if you're concerned about the look of your device. (And as an extra tip, should you change your mind, Sharpie comes off easily with dry erase markers)
...or, just learn how to disable them. If you know your way around a soldering iron, you might be able to figure out how to open up your device and disable the stanby light yourself with these instructions.