9-volt LED Replacement Module Advice Needed

[Fiddler]

I own a couple of these Burnham Brothers scope-mounted shooting lights: http://www.burnhambrothers.com/product.asp?ProductID=18662
I like them the way they are, but am wondering if I can improve the extremely short battery life by replacing the standard bulbs with LED's.
I'm having trouble locating LED's which can stand up to 9-volts. I'd appreciate any advice.