There are build guides (and even ready-to-use RPM's) for openssl 1.0.2 on CentOS 6 elsewhere on this forum:
This works because openssl 1.0.2 is ABI compatible with 1.0.1 (newer versions aren't).
But let's be clear: anything you change on your CentOS 6 server is at your own risk, you should upgrade or replace it eventually.