I found out today that Sun has an alpha version of Java 1.6.0 64-bit for linux. Look here for Java SE 6 Update 12. I had been using IcedTea java and I disabled it before proceeding.
I downloaded the .bin file into my Download area and ran sudo ./jre-6u12-linux-x64.bin. This could have been done as a normal user. I then moved the jre1.6.0_12 folder to /opt/jre1.6.0_12. I looked through the files and tried what appeared to be the java plugin, but it didn’t work when I installed it in my ~/.mozilla/plugins folder. Searching the web led me to this post. After reading it, I did the following ln -s /opt/jre1.6.0_12/lib/amd64/libnpjp2.so ~/.mozilla/plugins/libnpjp2.so. This worked like a charm! .