On its face such a law would seem to violate both the Federal Constitution as well as the Constitution of the State of Tennessee. The first amendment to the U.S. Constitution, as applied to the states through the 14th amendment, states that: "Congress shall make no law respecting an establishment of religion..."
The Tennessee Constitution states: "Section 3. That all men have a natural and indefeasible right to worship Almighty God according to the dictates of their own conscience; that no man can of right be compelled to attend, erect, or support any place of worship, or to maintain any minister against his consent; that no human authority can, in any case whatever, control or interfere with the rights of conscience; and that no preference shall ever be given, by law, to any religious establishment or mode of worship."
Making one religious text a state's official book is essentially the definition of the establishment of religion in violation of the U.S. Constitution, and would similarly be a preferential treatment of the christian faith in violation of Tennessee's constitution. If this is not vetoed by the Governor, it will certainly be overturned by the courts. It doesn't matter if the law passed unanimously, it would still be unconstitutional and therefore invalid.