Or, this is an option:
and get the Linux RPM file. Wherever it downloads, go to the directory and as root run it like a shell script
[root@localhost ~]# sh jre-6u13-linux-i586-rpm.bin
That will install it to your machine, but that does not force it to be used.
/usr/sbin/alternatives --install /usr/bin/java java /usr/java/default/bin/java 20000
And for Firefox:
/usr/sbin/alternatives --install /usr/lib/mozilla/plugins/libjavaplugin.so \
libjavaplugin.so /usr/java/default/plugin/i386/ns7/libjavaplugin_oji.so 20000
And then log out and log back in just to be sure, though you shouldn't have to. That will have the proprietary Java Runtime Environment installed and being used for both Firefox and your base install. Hope that helps.