The observation of localized stationary structures, coined oscillons, in granular media has evoked much interest. By parametric excitation of clay suspensions, we demonstrate a hysteretic transition to oscillon-type states in a nongranular medium. When the symmetry of up-down reflection+ time translation is lost, these states undergo a transition to propagating localized states previously seen in Newtonian fluids. These observations are in accord with recent theoretical predictions of sufficient conditions for oscillon formation. In addition, a novel measurement technique for the effective suspension viscosity demonstrates their shear-thinning properties.