When you run Paragon Chat, it'll ask you to login to chat before running the COH client. Instead of that, click on the blue folder button. It will open an Explorer Window where Paragon Chat is at. Open the Database folder and copy the contents of that folder somewhere safe, like a USB drive. (The most important file is ParagonChat.db.)
That's it. You just backed up Paragon Chat. To restore it, install Paragon Chat on another system, and click the blue folder again on the Sign in Window. Open Database and paste the files back. Overwrite what's there if needed.
Then close Explorer and log in normally.