Have you paid for more than half of the child's expenses and has the child lived with you for 12 months? If so then you will be able to claim her as a qualifying relative. If she hasn't lived with you for the full year you can't claim her at all. If they are receiving government assistance of any kind, such as food stamps, then you have to include that as part of the care the mother is providing when determining if you provided half of her care.

If your sister lives with you and you don't charge rent and buy food and such that goes to the care of both of them you may actually be able to claim both of them as dependents under the qualifying relatives rule. Your sister would have had to earn less than $3600 for the year to qualify, the other rules are the same as above.

Also, depending on the custody papers the father may be entitled to claim the child instead since he is paying child support.

What expenses have you been paying for that benefit only your niece, but not your sister? Do they live with you? We're going to need more information to give you an answer. Your sister not being able to benefit from filing a tax return this year doesn't mean she can simply lend her dependent out to someone who "helps".

For example, if you gave your niece ballet lessons for her birthday and a new winter coat and boots for Christmas, those kids of things are gifts and not exactly an indication that you are supporting the child and paying more than half of her support yourself.