We now have nginx SSL proxies in front of the beta caches (Bug T38648). We still have to fix the certificate (that is *.wmflabs.org for now).
We need certificates generated by 'Labs CA' for the entries listed in role::protoproxy::ssl::beta and some more. I guess the easiest would be to create *.beta.wmflabs.org cert that will also contains the following DNS entries:
*.wikimedia.beta.wmflabs.org
*.wikibooks.beta.wmflabs.org
*.wikinews.beta.wmflabs.org
*.wikipedia.beta.wmflabs.org
*.wikiquote.beta.wmflabs.org
*.wikisource.beta.wmflabs.org
*.wikiversity.beta.wmflabs.org
*.wikivoyage.beta.wmflabs.org
*.wiktionary.beta.wmflabs.org
And the mobile ones:
*.m.wikimedia.beta.wmflabs.org
*.m.wikibooks.beta.wmflabs.org
*.m.wikinews.beta.wmflabs.org
*.m.wikipedia.beta.wmflabs.org
*.m.wikiquote.beta.wmflabs.org
*.m.wikisource.beta.wmflabs.org
*.m.wikiversity.beta.wmflabs.org
*.m.wikivoyage.beta.wmflabs.org
*.m.wiktionary.beta.wmflabs.org
*.zero.wikipedia.beta.wmflabs.org
See Also:
T56065: Enable HTTPS on a Labs instance
T70387: Beta Cluster no longer listens for HTTPS
T71269: Give all members of the deployment-prep project sudo