Send a written request that the child(ren) be placed on a name check system. Send child(ren)'s names, dates and places of birth, plus Social Security Numbers (if you have them), and any other pertinent information (like a physical description), along with your name, address, and a phone number where you can be reached, to Passport Services. Make sure you sign the request. You can FAX the request letter to 1-202-955-0230.
More information on this topic is available here: Preventing International Move-Aways.