Either Mozilla or Galeon (and presumably other Mozilla derivatives)
are said to be able to use the Blackdown Group's Linux port of Sun's JRE
plug-in for Netscape Navigator/Communicator. The trick: You need to add
links from mozilla/plugins to the Sun Java installation directory.

Open-source alternatives to Sun's proprietary JRE:

Japhar http://www.japhar.org/oji.html
Kaffe OpenVM http://www.kaffe.org/ doesn't appear to have a Mozilla
plugin version, yet.

Both would speak to Mozilla via the Open Java Interface spec: