Expedited passports are available at regional offices, which include New York (Manhattan), to people that will be traveling within the next 14 days. You have to make an appointment via telephone, and the child and both parents (or consent as stated above) have to be present. You also have to show them your travel ticket or electronic itinerary to prove your travel date. I just did this about 3 months ago for my son and will only take 3 to 4 hours of your time at the passport office.
All the info that you can want on this subject, including how to make an appointment, office locations, fees, etc., can be found at
Passport Home