After a few failed starts getting Java to update via WSUS Package Publisher, I’ve taken one more try.  Here are the steps I used to successfully deploy Java 6 update 115.  The process should work for any Java version.

Download the latest Java installer either from the public site, or from Oracle Metalink if you are using a non-public copy.
Run the installer, but do not start the installation.  Navigate to “%LOCALAPPDATA%LowSunJava” and copy the jre1.x.x_xxx folder to another location.
Repeat for the x64 installer if needed.
Edit the MSI to disable the auto-updater, reboot, etc. per http://ivan.dretvich.com/2011/06/how-to-package-and-deploy-java-jre-1-6-0_26-via-group-policy/

Make a note of the product code while you are editing the MSI, you will need it later on.
I set the updater off, ie/firefox plugins on, accept eula by setting EULA=0, rebootyesno to no

Log into your WSUS server and copy the files over to your distribution holding folder.
Deploy via WSUS using https://community.spiceworks.com/how_to/122612-how-to-deploy-java-to-clients-using-wsus-package-publisher

Make sure you include the data1.cab and any relevant MST’s otherwise the install might not work.

Approve and test the deployment.