To parents of children under 14 (and/or unable to sign their name) or someone acting for a disabled person of any age....
8 CFR 103.2
(a)
(2) Signature . An applicant or petitioner must sign his or her application or petition. However, a parent or legal guardian may sign for a person who is less than 14 years old. A legal guardian may sign for a mentally incompetent person. By signing the application or petition, the applicant or petitioner, or parent or guardian certifies under penalty of perjury that the application or petition, and all evidence submitted with it, either at the time of filing or thereafter, is true and correct. Unless otherwise specified in this chapter, an acceptable signature on an application or petition that is being filed with the BCIS is one that is either handwritten or, for applications or petitions filed electronically as permitted by the instructions to the form, in electronic format. (Revised effective 5/29/03; 68 FR 23010 )
*** Below is what they say to do on a Certificate of Citizenship, so it is not a big stretch of the imagination to follow this procedure,***
In general anything "....shall be signed by the applicant unless the applicant is a child unable to sign his/her name, in which case the certificate shall be signed by the parent or guardian, and the signature shall read "(insert name of child) by (insert name of parent or guardian, indicating which)."
Jane Doe by John Doe, father/mother (sign YOUR normal signature and print her name and your relationship)