Small Business Fairness Act of 2010 - Amends the Small Business Act to permit a federal agency to count toward its federal small business procurement and services contracting goals a contract between that agency and a small business teaming arrangement entity, to the extent that the obligations of such entity are performed by a qualified HUBZone small business or a small business owned and controlled by service-disabled veterans, socially and economically disadvantaged individuals, or women. Includes as a qualified HUBZone small business an Alaska Native Corporation and a small business wholly owned by one or more Indian tribal governments.