We show that resonant coupling of synchrotron beams into suitable nanostructures can be used for the generation of coherent x-ray point sources. A two-dimensionally confining x-ray waveguide structure has been fabricated by e-beam lithography. By shining a parallel undulator beam onto the structure, a discrete set of resonant modes can be excited in the dielectric cavity, depending on the two orthogonal coupling angles between the beam and the waveguide interfaces. The resonant excitation of the modes is evidenced from the characteristic set of coupling angles as well as the observed far-field pattern. The x-ray nanostructure may be used as coherent x-ray point sources with a beam cross section in the nanometer range