I used this method for installing the latest java plugin on a CentOS 5.4 system.

Download latest java (jre-6u18-linux-x64.bin) from java.com.
I installed all my java versions in /usr/java. This is where I save the bin file downloaded.
cd /usr/java
chmod 744 jre-6u18-linux-x64.bin
To install java:

To install the plugin into your latest version of firefox:
cd /usr/lib64/firefox-3.0.16.
mkdir plugins #I had to create this directory.
ln -s /usr/java/jre1.6.0_18/lib/amd64/libnpjp2.so

Restart firefox.