If you have checked and you have the right SSN for your child, then there is a mismatch in the system somewhere and you cannot e-file. Someone else may have used your child's SSN on purpose or accidentally but you will have to print, sign and mail your return to claim your child.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.
Federal and state returns must be in separate envelopes and they are mailed to different addresses. Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.
Unfortunately you will most likely have to paper file as directed in this thread. Before doing that, double check that the date of birth entered was correct and that your dependent's name is written exactly as it is on his or her social security card. Sometimes, this may also be causing the rejection.