National Trauma Center Stabilization Act of 2009

National Trauma Center Stabilization Act of 2009 - Amends the Public Health Service Act to replace the trauma center grant program that provided for operating expenses for trauma centers incurring substantial uncompensated costs due to violence from illicit trafficking in drugs with a program to provide grants to public, nonprofit, Indian Health Service, Indian tribal, and urban Indian trauma centers to assist in defraying substantial uncompensated care costs, further the core mission of such trauma centers, and provide emergency relief to trauma centers at risk of closing or centers operating in an area where a closing has occurred within their primary service area. Sets forth qualifications for grantees and provisions governing the amount of the grant award.

Directs the Secretary of Health and Human Services (HHS) to provide funding to states for grants to eligible entities to: (1) improve the availability of trauma services in underserved areas; (2) address trauma center overcrowding; (3) enhance trauma surge capacity; (4) address shortages of trauma surgeons and certain other trauma-related physician subspecialties; and (5) improve trauma service coordination and the appropriate transport of trauma patients to trauma centers. Requires the Secretary to distribute amounts based on a state's population.