Here are a few possibilities:
Use the properties service. See rghe properties-service.xml file in the deploy directory.
Place the properties file in the conf directory. That directory is in the classpath for every web app.
I ended up using a managed-bean-property in one project, which works really well.
But I'm still looking for a method in my "unmanged" bean (see my other thread).
I will look into what you suggest.