Civil Rights Tax Relief Act of 2009 - Amends the Internal Revenue Code to allow: (1) an exclusion from gross income for amounts received (either backpay or frontpay or punitive damages) on account of an unlawful discrimination claim; (2) income averaging for backpay and frontpay amounts received from such claims, and (3) an exemption from the alternative minimum tax (AMT) for any tax benefit resulting from the income averaging of amounts received from an unlawful discrimination claim.