For 2020:
There were two rounds of stimulus payments in Summer 2020 and Winter 2021, of $500 for each qualifying child dependent. If you did not get the stimulus check, you could get a rebate if you claimed the children as dependents on your 2020 tax return. That's the end. If you did not claim them as dependents on your 2020 tax return, you can't get a stimulus or rebate.
For 2021:
You can't get a stimulus check ($1400) for a dependent that you plan to claim in 2021 but did not claim in 2020. You can claim a rebate on your 2021 tax return instead.
Congress has also authorized payment of an advanced child tax credit ($300 per month) for each qualifying dependent. This is separate from the stimulus and has different rules. The IRS has said they will set up a web site where you can register a dependent for the payment if you did not claim them in 2020, but that web site is not ready yet. If you can't get the advance payment or only get a partial payment because of delayed sign-up, you will get the rest of the credit on your tax return.
