On my CentOS 6 machines (which are few now as it approaches EoL) there is no site_perl. Modules installed from source go in /usr/local/share/perl5/ and modules installed from packages go in /usr/lib64/perl5/vendor_perl/.

Another package that I have been been trying to run requires the presence of this path perl5.10/lib/site_perl.

Perhaps this "another package" is buggy or is not designed to work on CentOS 6? If you provide full details, or better yet an SSCCE, somebody may be able to help you further.