This is a great page on how to build OpenSSL 1.0.1 for RHEL/CentOS 6.x:
https://www.ptudor.net/linux/openssl/
This has been ported from the work done on Fedora OpenSSL (https://admin.fedoraproject.org/pkgdb/acls/name/openssl and http://pkgs.fedoraproject.org/cgit/openssl.git/). FIPS has been removed for ease of compiling.
Have been running this on our dev environment for a few days and seems to be secure. OpenSSL 1.0.1 adds TLS 1.1/1.2 (changelog here: http://www.openssl.org/news/changelog.html)