I'd say its totally impossible to only analyze that stack trace and give you an "answer". At least you should include some code snippets from your project.
Okay, what I think can be the problem is this: The Tyrus libraries are not distributed with the Application Client Container. Locally then, first class that the class loader wants to load.. will fail.
So, right-click your project and select Properties. Select Libraries. Make sure your library has been put beneath the Run tab. If not, click on the Add Library... button you find in this tab and follow procedure!
Hope this was of help to you. If not, review this tutorial on how to package a JavaFX client and have him launched through Java Web Start. The application client in this tutorial depends on external libraries too and you might find something useful in there.