The only state's right at issue was slavery.
Although the northern states were a little torqued off over the Fugitive Slave Act, which made a mockery of states' rights.
Walt
There were many salient issues involving state's rights versus the federal government which in turn contributed to the war: These included the imposition and impact of various tarrifs...Banking regulations and conflicts....Indian affairs(a major problem of the times). Source Columbia Encylopedia..6th ed.