COBRA Displaced Family Amendments of 1991 - Amends the Internal Revenue Code, the Employee Retirement Income Security Act of 1974 (ERISA), and the Public Health Service Act (the Acts) to declare that specified provisions relating to the required period of group health plan continuation coverage do not apply to the qualifying events of death, divorce, or legal separation involving a beneficiary who is 50 years old or older. Requires that coverage continue until the 23rd birthday, or 36 months after the qualifying event, whichever is later, for an individual who is a dependent child beneficiary at the time of such an event involving a covered employee 50 years old or older.

Amends the Acts to modify: (1) the termination of extended coverage for disability and the general rule for other qualifying events, as they relate to the maximum required period of continuation coverage; and (2) dates by which certain notices must be given.

Amends the Acts to require that notice of the option to enroll under a conversion plan be given during the 120-day period ending 60 days before the expiration of the continuation coverage. (Current law requires such notice be given during the 180-day period ending on the expiration date of the continuation coverage.)