Well, since no Java vendor is about to release a J2SE implementation for the Zaurus (how I wish I was wrong!), you are left with the DIY approach: using open-source, non-licensed JVMs, such as kaffe or jamvm, together with
GNU classpath which is an open-source implementation of the standard APIs. You will get something similar to 1.2 rather than 1.4 but it's better than nothing, I suppose.
(Just to make things clear: a Java Virtual Machine is the engine that runs Java code while APIs are the basic building blocks for Java applications, usually themselves written in Java mixed with native code).
The classpath project seems to be coming along - and they have very nice compatibility charts showing what exactly is missing vis-a-vis various versions of Java. Swing seems to be about 70% complete vs. 1.2. As for
JVMs, last time I checked none of them was really decent but things may have changed. I would be quite interested to hear whether anyone has got any of this working.