The United States doesn't have any special requirements or exceptions for a baby's passport photos. They must adhere to the same criteria as an adult's photos.
The Department of State provides guidelines for taking good passport photos. Note that the photos can't be more than 6 months old and that your baby's face must be in focus. You can't use standard baby pictures, including those taken at the hospital.
Baby photographers will usually cost more than passport photo services. However, baby photographers may be better at getting your baby to look at the camera, which could help save you time and frustration. Make sure the photographer understands the government's requirements for passport photos.
Passport Photo Services
Many drugstores, copy shops, and private packing and mailing stores offer passport photo services. These are usually inexpensive, and the photographers are trained to take photographs that meet the government's requirements. Call ahead to ask if they are able to accommodate babies.
Photos at Home
You can take your baby's passport photos at home, but make sure they meet the government's standards. No pacifiers; hats; or means of support, such as an infant seat or your hand, can be visible in the photo. The easiest way to accomplish this is to place a white sheet over the infant seat, put your baby in the seat and take the picture.