never store sensitive data like API keys in a repository. Or you can do that but encrypt it so that nobody which can view your repo (even if it's private) can use that data immediately. It's like storing passwords in plaintext in a DB. Every (DB) admin will tell you: Don't/Never do that.
I've recently also have to do with this problems while doing server setup with a private repo. I'm using Ansible and Ansible Vault to encrypt sensitive data and the encryption key itself is only accessible (a password safe) to certain members of our team http://docs.ansible.com/ansible/playbooks_vault.html
see, the whole repo is accessible to the members of the team that are allowed to see the secret - basically the two folks that have root on the machine anyways. There's very limited use in encrypting the repo. There are no SSL keys or any secrets that would require tight security. It's basically our newrelic and some other api keys for reporting services. Even if that repo would be breached you could only start sending fake data to those services.
I'm more concerned about someone hacking the machine than someone hacking github to access the repo and retrieve the newrelic key from there.
I've recently also have to do with this problems while doing server setup with a private repo. I'm using Ansible and Ansible Vault to encrypt sensitive data and the encryption key itself is only accessible (a password safe) to certain members of our team http://docs.ansible.com/ansible/playbooks_vault.html