Children's Asthma Relief Act of 1999 - Amends title V (Maternal and Child Health Services) of the Social Security Act (SSA) to establish an asthma treatment grants program providing comprehensive asthma services for children and other individuals. Authorizes appropriations.

Directs the Secretary of Health and Human Services to encourage States to implement plans to carry out activities to assist children with respect to asthma in accordance with the guidelines of the National Asthma Education and Prevention Program and the National Heart, Lung, and Blood Institute (Institute).

Provides that if a State CHIP plan under SSA title XXI (Children's Health Insurance) (CHIP) provides for such activities to the Secretary's satisfaction, the Secretary shall make a grant to assist the State in carrying them out. Sets forth certain matching funds requirements. Authorizes appropriations.

Amends the Public Health Service Act to include, within the preventive health and health services block grant, any systems for reducing asthma and asthma-related illnesses, especially with regard to children, through urban cockroach pest management in public facilities that minimizes or avoids chemical pesticides through a combination of appropriate practices involving the maintenance, cleaning, and monitoring of such sites.

Directs the Institute Director to: (1) identify all Federal programs carrying out asthma-related activities; (2) develop a Federal plan for responding to asthma; and (3) submit recommendations to Congress on ways to strengthen and improve the coordination of such activities. Authorizes appropriations.

Requires the Director of the Centers for Disease Control and Prevention to: (1) conduct local asthma surveillance activities to collect data on the prevalence and severity of asthma and the quality of asthma management; and (2) compile and publish annually data on the prevalence of children suffering from asthma in each State, and the childhood mortality rate associated with asthma nationally and in each State.