Java2Script does not provide JavaScript Swing library. It currently provide Java2Script SWT library.
Some years ago, I tried to use swingwt (
http://swingwt.sourceforge.net/ ) to build Java2Script Swing library. It seemed the job is feasible but need a lot of time. As I did not have enough time to do so, I stopped.
Not sure about your goal. If you want to support converting Applet to web, you may rely on tools. Maybe you means that once you have the Applet library in JavaScript, you can write your web app in JavaScript instead Java. In such cases, I suggest you using existed JavaScript library instead of creating another one from existed Java sources. JavaScript language model is different from Java language model. You may come up with many difficulties and may waste your time. Existing YUI, may be your choice.