I have had a rat problem recently as well. I tried one of the rat zappers - no luck. I tried old fashioned rat traps with peanut butter - no luck. The way I handle it now is with a pellet gun. I wait until an hour after sundown, open the main coop door, and can sometimes get get one. I also go out about an hour before sunup and the same thing. This has reduced the population, but we still find droppings so I still go out at those times even though on many occassions I cannot find them. In most instances, it only seems to be one single rat at a time in the coop. Sometimes I miss. They can move pretty fast when they get in panic mode. My girls (and boy) are now used the sound of the air rifle and it doesn't seem to bother them anymore. It did the first couple of times.
I have found that closing the pop door also helps in our situation. It seems the rats come in through the pop door, but exit through the nest boxes. I have yet to see one in the coop when I have the pop door closed at night. I haven't proven this theory yet though.