We report the magnetic structure of the two magnetically ordered phases of Co-3(OH)(2)(C4O4)(2), a coordination polymer that consists of a triangular framework decorated with anisotropic Co(II) ions. Neutron diffraction experiments allow us to confirm that the magnetic behavior changes upon dehydration and reveal the complex phase behavior of this system, relative to the hydrated compound Co-3(OH)(2)(C4O4)(2)center dot 3H(2)O. One phase is shown to display spin idle behavior, where only a fraction of the moments order at intermediate temperatures, while at the lowest temperatures the system orders fully, in this case with a net magnetic moment. This novel magnetic behavior is discussed within the framework of a simple Hamiltonian and representational analysis and rationalizes this multiphase behavior by considering the combination of frustration and anisotropy. The change in behavior on dehydration is also rationalized with respect to the changes in the single-ion anisotropy of the cobalt.