What are you starting with?  SSA?  Something else?  Googling for
"register allocation algorithm" will give you a good look at the
available algorithms.  The JVM has little to do with it by the point
you're allocating registers, so don't bother restricting your research
to Java-specific information.

The one thing that might be slightly Java-specific is that because JITs
often need to run quickly, you'll need a fast-running algorithm even at
the expense of a good allocation.