Adoption Awareness Act of 1999 - Amends the Public Health Service Act to direct the Secretary of Health and Human Services to make grants to national adoption organizations for programs to train the staff of eligible health centers in providing adoption counseling to pregnant women and infertile married couples.

Makes it a condition for receipt of such a grant that the national adoption organization involved agree to make reasonable efforts to ensure that the eligible health centers with respect to which training under the grant is provided include centers that: (1) receive grants relating to voluntary family planning projects; (2) receive grants relating to community health centers, migrant health centers, and centers regarding homeless individuals and residents of public housing; (3) receive grants for the provision of services in schools; and (4) do not perform or make referrals for abortions, or provide or make referrals for counseling that presents abortion as an option.

Directs the Secretary to require programs providing voluntary family planning services with such a grant to provide nondirective counseling and referrals regarding prenatal care and delivery, infant care, foster care, and adoption.

Makes religious organizations eligible for such grants without discrimination and mandates their independence from Federal, State, and local governments, providing certain safeguards to ensure such independence.

Provides the beneficiaries of assistance from religious organizations with certain rights, including the right not to be discriminated against by the religious organization.

Authorizes appropriations.