No. The CARES Act, which provides an additional $500 for child dependents, uses the tax code definition of a child—any child you claim as a dependent on your taxes must be under 17 years of age as of the end of 2019. (The Consolidated Appropriations Act, which provides a $600 additional child payment, follows the same rules).
However, if you are not able to claim them as a dependent for 2020 and if they file their own individual tax return, your child could receive both the $1,200 CARES Act stimulus amount and the $600 Consolidated Appropriations Act payment (EIP1 and EIP2, respectively) via the Recovery Rebate Credit.
Note: If your child, age 17 or older, files his or her own taxes, they still will not receive a stimulus payment as long as you are able to claim them as a dependent; their “Dependent of Another” status disqualifies them from receiving payment.