So you aren't allowed to use Jython for the production code you develop at work. You can, instead, use it to help you on your daily tasks and activities writing that Java code. The question is: How do you use Jython and how did that help your development and/or productivity?
I run a Jython command line, and dynamically create/interrogate my classes on the command line. I find that very effective for determining how classes will respond to various inputs (usually these get coded up into tests and the like).
I also found this very useful for learning Swing - dynamically resizing/repacking and adding/removing components.
You can do the same with other Java scripting languages (e.g. BeanShell) but Jython's the one I picked up on and used first.