I\'m trying to create a stage that doesn\'t appear on the Windows task bar and is undecorated (no borders and no close/minimize/maximize buttons). My end goal is to create a
JavaFX doesn't support the feature you request
You cannot do what you are asking (not show a task bar icon for an undecorated or transparent stage) using just the core Java 8 classes.
If you wish, file a feature request for this in the JavaFX issue tracker.
You could write some native JNI code and perhaps tell Windows not to display a task bar icon for your application. I do not know how you would do this.
Suggestion on task bar icons
I think it is fairly standard windowing toolkit behaviour to show the main application window in the task bar when the main application window is not hidden, so I suggest not trying to circumvent that standard behaviour.
Suggestion on notifications and tray icons
This isn't directly related to your question title, but is just comment on the end goal of your task - notifications for tray icons.
Most tray based applications I have seen don't have a task bar icon when the window associated with the tray icon is hidden, but do have a task bar icon when the window associated with the tray icon is displayed - so I suggest you stick with that setup.
Also, notifications are a standard part of the system tray icon infrastructure itself, so I suggest you use the standard mechanisms for system tray icon notifications, rather than using your own. This will also allow the user to configure whether the tray icon and it's notifications are shown using the standard OS tray icon and notification management UIs.
I created a sample application which uses the AWT SystemTray API to provide a System tray for a JavaFX application which uses some of the suggestions from this section. You can try it out if you like.
Full system tray support will come to JavaFX (probably with Java 9) when RT-17503 Provide system tray support is implemented.