Is it possible to change the application icon using JavaFX, or does it have to be done using Swing?
Assuming your stage is "stage" and the file is on the filesystem:
stage.getIcons().add(new Image("file:icon.png"));
As per the comment below, if it's wrapped in a containing jar you'll need to use the following approach instead:
stage.getIcons().add(new Image(<yourclassname>.class.getResourceAsStream("icon.png")));