If e-filing the returns, your electronic signature is part of the e-file process just like filing your own return works.
If you are mailing them in and the child is able to sign they can sign.
If the child is unable to sign, then, if you are the guardian, you can sign the child's name followed the words "By (your signature) guardian for minor child." If someone else is the parent or guardian then they will need to sign for the child as noted.
Here is an IRS reference.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"