the current java 1.7 dose NOT use the old java 1.6 plugin
also the GPL'ed OpenJDK is likley what you already have installed
and for that search yum
yum search java
and that should bring up a list
also with this being RHEL 6 , and an older version at that -- you ARE paying red hat to LOCK it at the older 6.3 version ???
so with the support contract you did buy you have access to the knowlage base
the FULL instructions for moving from OpenJDK 1.7
to the NOW unsupported
Oracle Java1.6 is in there
the current is RHEL 6.4
Red Hat really is NOT free , you DO need to buy the REQUIRED support contract !
For a single desktop install you can buy the license
and if you have to ask , then likely you will NEED the standard 1 year for $299( USD ) PER YEAR