I dropped a few fonts in there, but logging all the font family names Java knows about, I only see serif, sans-serif monospaced, dialog, default, etc.
I tried adding another name to font.properties in /usr/java/lib, but that did not work.
Then I just replaced the monospace section with my own font. I think it worked. I say "I think", because I'm not a font expert. It seems to look slightly different, but I might be imagining stuff.