A disabled cousin would only qualify as what is called a Qualifying Relative. They are not closely related enough to qualify you for the Earned Income Credit, nor would they qualify you for any child-related credits. The most you would receive is a deduction of $4050 for their exemption.
A deduction like this can only lower the amount of income on which you pay tax, and can get you back some of the tax you had taken out during the year. If you are already getting a refund of the tax you had taken out, you can't get anymore than that back for claiming them as a dependent.
