For lights on the outside of objects, like routers, modems, cable boxes, ect that never go of I have always used black electrical tape to cover them. That would be an option as long as it doesn't cover any vents. Low power LEDs can get warm, but not hot so I wouldn't worry about that.
You could simply paint over the "bulb" of the LED if it is exposed. Pretty much any kind of paint would work, except the colors that are made from metallic elements which can be conductive (mostly paints that mimic metals).
Are you trying to make it look pretty or just trying to cut down on the light bleed? I can't imagine that globs of blu tak look very good, plus I would worry about it sliding off and falling into a fan or something. Careful painting sounds like it might be your best solution. A small hobby brush and a .25 oz bottle of matte black paint would cost literally $2. If you can be without your pc for like a day while it dries it would be a good solution.
Pics might help, I'm suggesting that you actually paint the LED itself not a portion of the mobo, I wouldn't paint on a circuit board or wad of blu tac on a circuit board for that matter. Just because something is non conductive doesn't mean it's meant to be put in your PC case, you could bury your motherboard in sawdust, that's not conductive.