There are two approaches to how to do this. The first is simply get artillery at tech 8 as a nation that borders the nation controlling Berlin. Attack the nation and do the barrage.
But, if your nation isn't able to get a CB against the nation, you can do it during the Religious Leagues (which require the Art of War DLC). Join the opposing side of the nation and wait for the war to start. Push to Berlin to siege it and use the barrage. Really great for nations like France and Russia since the HRE tends to prevent outsiders attacking members.