You file her as Someone else I support / OTHER.
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 a residence test. Only a QC qualifies the taxpayer for the Earned Income Credit, the Child Tax Credit.
A cousin is not considered closely related and therefore cannot be a QC.
A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:
1. Closely Related OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4,050 (2016)
3. The taxpayer must have provided more than 1/2 his support
4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer