Coherent state path integrals without resolutions of unity

From the very beginning, coherent state path integrals have always relied o n a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a st of "coherent states" spans the same s pace but loses its resolution of unity,and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-sp ace path integral representation in essentially the same form as if it had a resolution of unity. Our examples are toy models of similar situations th at arise in current studies of quantum gravity.