Welcome to Android Central! What about the stock Jellybean Alarm Clock--do you have that? Just open Clock, and tap the menu button, select Night Mode.
You could also install an app that dims the screen further than the stock controls usually allow. Try Screen Filter or Screen Dimmer. Keep in mind, though, that when you dim the screen with these apps, you might encounter a weird glitch with Amazon Appstore that prevents you from pressing the Install button when trying to download and install an app. This resolves once you turn off the dimmer.