The dependents on your return will need a social security number to efile. If they do not have one, you will have to leave the section blank and file your return by mail.
Per the IRS
"If you have a religious or conscience-based objection to securing a Taxpayer identification Number for the dependents or exemptions, please forward a statement outlining your objection and documentation from the following lists to verify the dependents."
For the full article regarding exemptions for Amish dependents, see the link below. The information pertaining to your situation is in section 21.6.1.5.1 (10-01-2013).
https://www.irs.gov/irm/part21/irm_21-006-001r.html