I’ve figured out how to purchase and use many other specific cleric domains, but I cannot locate the pain domain. Does anyone know if it’s accessible at all on this site?

I don't believe the pain domain exist in a WotC publication.  It sounds like a third party publisher domain, and a quick google seems to indicate that too.  If you have the publication it appears in, the Homebrew Subforum can guide you through home brewing the domain and adding it to your homebrew collection.