You'll need to ensure that they have the JVM installed. I think some versions of OS 9 did not ship with a JVM.
Also, you may need to make sure your App limits itself to an older version of
Java. I'm pretty sure the OS 9 JVMs didn't make it to 1.3; I'm not sure if they even made it to 1.2.
Out of curiousity, why do you need to run on OS 9? I think most Mac folks have upgraded to some version of OS X by now.