Family Violence Prevention and Services Improvement Act of 2019 This bill modifies, expands, and reauthorizes through FY2024 the Family Violence and Prevention Services program, which funds emergency shelters and supports related assistance for victims of domestic violence. Specifically, the bill requires the Department of Health and Human Services (HHS) to award grants and enter cooperative agreements with state and tribal domestic violence coalitions, and community-based organizations, to support prevention services. Depending on the type of organization, grant recipients must use funding to (1) provide technical assistance; (2) promote evidence-informed prevention strategies; (3) implement coordinated, community responses to reduce risk factors for family violence; and (4) develop prevention partnership strategies, among other uses. Further, HHS must award specified grants to organizations that provide population-specific services in underserved communities and to community-based organizations that provide culturally competent domestic violence services to racial and ethnic minority groups. The bill also establishes a grants program for tribal domestic violence coalitions to support the provision of local, tribal, family domestic or dating violence services and requires HHS to award a grant for the administration of a hotline dedicated to serving Indians affected by domestic violence. In addition, the bill modifies certain program-wide definitions; changes the requirements for specified grant applications, eligibility criteria, and use of funds; and makes other technical revisions.