N-600被拒之后不能再次申请N-600，所以申请I-290B是正确的，如果他想要那个certificate

看N-600 instructions：

Who Should Not File Form N-600?

5. You already filed Form N-600 and received a decision from USCIS on that previously filed Form N-600. USCIS will reject (not accept) any subsequently filed Form N-600. Review your Form N-600 denial notice for more information.

和8 CFR 320.5(c)：

Subsequent application.  After an application for a certificate of citizenship has been denied and the time for appeal has expired, USCIS will reject a subsequent application submitted by the same individual and the applicant will be instructed to submit a motion for reopening or reconsideration in accordance with 8 CFR 103.5. The motion must be accompanied by the rejected application and the fee specified in 8 CFR 106.2.

当然，你也可以直接不要Certificate of Citizenship；只申请美国护照就行了。Certificate of Citizenship又贵又没有什么用处是护照没有的。

还有，要确定一个东西：孩子是18岁之前拿到绿卡的，对吧？