A stronger argument to support federal rather than state enforcement of civil rights is that civil rights are guaranteed under the U.S. Constitution, and are therefore uniform throughout the U.S. Furthermore, as they are rights guaranteed under the Constitution, states have no right under the constitution to supercede them. Article Six of the Constitution reads in part:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
All judges, state and federal, take an oath to preserve, protect and defend the Constitution of the United States. However, the ultimate authority to protect the Civil Liberties granted under the Constitution of necessity much lie with the Federal system. For that reason, it is a far more appropriate forum for the Federal Government to exercise sovereignty over these matters.
To make this argument, you should focus on the idea that civil rights are fundamental human rights. For example, non-white people have a fundamental human right to be treated equally by the law. This is not something that should be left up to the states. All people who are American should have the same basic rights. It should not be possible for one state to deny rights to certain unpopular groups of people. It is okay for the states to have different rules on relatively trivial things like tax rates or speed limits. But it is not acceptable for states to have different laws regarding fundamental human rights.