How to inject a parameter into a singleton class?

I have a singleton class which has been adopted so that the super method requires now an additional parameter, in my example it is set to foobar.

public class MySingleton        
{

private static final long serialVersionUID = -6053739985096001185L;
private static MySingleton SINGLETON = new MySingleton();

public static MySingleton getInstance() {
    return SINGLETON;
}

private MySingleton() {
    super( MySingleton.class, "foobar" );
}

}

My problem how can I inject this parameter to the this singleton class. The previous version of the private constructor looked like this

private MySingleton() {
     super( MySingleton.class );
}

To be more concrete my app will run on a tomcat server and I want to inject the context name of my application into this singleton, because this will extract some configuration properties with this name and such stuff. Would be a context listener the right choice but also then how can i inject the context name into the singleton?