Look into having your parents' marriage registered. There's no exception to the marriage certificate requirement as it seems marriages can be late-registered in India under the Hindu Marriage Act or the Special Marriage Act. From https://travel.state.gov/content/travel/en/us-visas/Visa-Reciprocity-and-Civil-Documents-by-Country/India.html --
Registration Criteria: Prior to 2006, marriages by Hindus, Buddhists, Jains, or Sikhs were not required to be registered, but may have been voluntarily registered under the Hindu Marriage Act of 1955. As of 2006, it is mandatory to register all marriages. In India, a marriage can either be registered under the Hindu Marriage Act of 1955 or under the Special Marriage Act of 1954. For marriages registered at government offices under the Special Marriage Act, the certificate will be issued by the Registrar only if the bride and groom personally appear before the official and pay the required fee. For other marriages that are required to be registered with government authorities under the Hindu Marriage Act of 1955, registration criteria vary by authority.
Procedure for Obtaining: Varies for each authority.
Certified Copies Available: There are no certified copies available.
Alternate Documents: See comments section.
Exceptions: None
Comments: Hindu Marriage Act is applicable to Hindus, whereas the Special Marriage Act is applicable to all citizens of India irrespective of their religion. Please note that marriages by Hindus, Buddhists, Jains, or Sikhs may be voluntarily registered under the Hindu Marriage Act of 1955.