Short post.
To install cpanminus on a CentOS 6 server, I ended up having to use the following command:

wget -O - | perl - --sudo App::cpanminus

The curl version of the command on the cpanminus website doesn’t work because the cipher used by libcurl is now blocked because of POODLE.  RedHat/CentOS haven’t released an updated curl that fixes the problem.