Well, just combine everything in $JAVA_HOME/jreinto your distribution (presumably the Zip/ file TAR), and then refer to your scripts (i.e. use the executable javaunder $JRE_HOME/binto run the java program).
Remember that if you do this, you will have to provide different distributions for different target platforms (Windows, OSX, Linux, etc.) and architectures (or one bloated uber distribution, of course, but no one will thank you for that!).