You may be eligible to claim both your niece and her son as dependents on your return. In order to claim someone as your dependent, the person must be:

1. Either your qualifying child or qualifying relative
2. A U.S. citizen, U.S. resident, U.S. national or a resident of Canada or Mexico
3. Unmarried or, if married, not filing a joint return or only filing a joint return to claim a refund of income tax withheld or estimated tax paid.

Additionally, you must meet the dependent taxpayer test. If you can be claimed as a dependent by another person, you can't claim anyone else as a dependent. If your niece can be claimed by you as your dependent, your niece cannot claim her son as a dependent of her own. 

The requirements for a qualifying child and a qualifying relative, as well as additional information regarding these tests, can be found in Publication 501, Dependents, Standard Deduction and Filing Information.