After reviewing this exact issue (https://github.com/jupyterhub/binderhub/issues/237) it seems that the functionality for this has been implemented with this merged pull request (https://github.com/jupyterhub/binderhub/pull/671).
However I can not seem to find guidance in the docs or elsewhere which explains what should go into the secrets.yml
file or if there are other steps required in order to use Binder with private Github repos (Apologies if I have missed the obvious -- complete Binder noobie here)
Link to my same question in the original issue: https://github.com/jupyterhub/binderhub/issues/237#issuecomment-462711995