Yes, they can prove that they live together for a long time by giving the documents such as joint bank account papers, bills that mention their names, any property ownership that mentions their full name in that document, and some photos you may include from their livesThank you.
One more thing do we have to provide marriage certificate? because they haven't register their marriage. Can we provide any other document?
Finally make sure they do an Affidavit before a Notary or Lawyer by mentioning all details about their lives and personal information along with Sponsor's full details.
Good luck