Select "My Child".
Cousins are not considered "closely related" for tax purposes, and normally you cannot claim a cousin as a "qualifying child".**
But, "legal guardianship" makes them your "foster children". Note that at the box where you check "my child", it says "(includes adopted, foster and stepchildren)".
**There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each. A cousin could normally only be considered under the qualifying relative rules. https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...