Getting a emergency child's passport can be tricky to say the least. You will need both parents to show up in person at a regional passport agency but first you will need to be traveling internationally in the next 14 days. Then you will need to make an appointment via automated telephone system at
18774872778. If you can't get an appointment or rather not spend the day waiting in lines you can also use a registered passport courier like Prompt Passports to do all the leg work and get your child's passport in as little as 8 hours.