My employer has a web application I need to use from home, that only works with a specific obsolete version of Java and range of obsolete versions of Firefox.

It must be used in the main OS, not a virtual machine.

I use Java in Firefox for other purposes that depend on having more recent versions, so I want to somehow install the obsolete ones as extra copies, not as the defaults.

I'm still trying to find out the exact Java version I'm required to use and the "any version before" rule for Firefox. But once I have that info, I don't know how to get two different versions to coexist.

Another employee (using a different Linux) uses SeaMonkey instead of Firefox for the obsolete version. Would that make sense on Centos 7?

You can have as many java versions as you want, installed at the same time.
Use the /etc/alternatives/ mechanism to switch java version.
Example :
# /usr/sbin/alternatives --install /usr/bin/java java /usr/java/jdk1.6.0_37/bin/java 2
Select :
# /usr/sbin/alternatives --config java


You can also have several versions of firefox, seamonkey.
Example :
$ cd /usr/local/
# mkdir 3 && cd 3/
# tar xvf firefox-3***.tar.gz
# cd /usr/local/bin/
# ln -s /usr/local/3/firefox/firefox firefox3
... Close all running firefox.
And save your current ~/.mozilla settings to a backup ( backup folder/.)
Start the old firefox with $ firefox3

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