In order to qualify for Emergency or Expedited service, the birth must be registered and you must provide proof of urgency along with your complete and correct applications form and fee.
Proof of Urgency may include:
A medical emergency
A letter confirming new employment
A letter from a consulate or embassy confirming an appointment
Airline tickets
A letter confirming an appointment for an immigration hearing
Travel reservations
A wedding invitation, where the applicant is the bride or groom