We report vibrational spectra of the cryogenically cooled H9O4+ cation along with those of the D-2 tagged HD8O4+ isotopomers using two variations on a two-color, IR-IR double-resonance photoexcitation scheme. The spectrum of the isolated H9O4+ ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the "Eigen" cation, the H3O+center dot(H2O)(3) isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD8O4+ isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H3O+center dot(H2O)(3) isotopologue. The feature appears with a diffuse band similar to 380 cm(-1) above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD2O+ core and one of the solvating water molecules. These trends are analyzed with anharmonic. calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations.