Well you could investigate the Java Plug-In Deployment Rule Set feature in Oracle's Java deployment documentation.
This involves buying a code signing certificate and deploying signed files to all client system's JREs via some other means (e.g. administrative push), so it is too painful for many sites to consider.
For most users the dialog noted here is just part of using the Java Plug-In these days. Oracle has at least reduced the frequency of this dialog's appearance. I believe it only appears once a day (or OS login, whichever occurs first) now.