Stop UN Support for Assad Act of 2019 This bill prohibits U.S. funding for United Nations (U.N.) programs in Syria unless the Department of State certifies that certain conditions are met. Specifically, no such funding may be provided unless the State Department certifies that any U.N. program in Syria with U.S. funding (1) is delivered impartially to the areas of greatest need; (2) does not directly provide material support to Syria's government or related entities; (3) adheres to human-rights-related requirements for U.N. suppliers; and (4) is vetted by an independent review mechanism, if the program involves contracts in territory controlled by Syria's government. Funding withheld from the U.N. under this bill shall be made available to the U.S. Agency for International Development's Office of Foreign Disaster Assistance for assistance to populations in Syria in need.