We use over a decade of geodetic VLBI data to estimate parameters in a resonance expansion of the frequency dependence of the tidal h2 Love number within the diurnal band. The resonance is associated with the retrograde free core nutation (RFCN). We obtain a value for the real part of the resonance strength of (-0.27¿0.03)¿10-3; a value of -0.19¿10-3 is predicted theoretically. Uncertainties in the VLBI estimates of the body tide radial displacement amplitudes are approximately 0.5 mm (1.1 mm for the K1 frequency), but they do not yield sufficiently small Love number uncertainties for placing useful constraints on the frequency of the RFCN, given the much smaller uncertainties obtained from independent analyses using nutation or gravimetric data. We also consider the imaginary part of the tidal h2 Love number. The estimated imaginary part of the resonance strength is (0.00¿0.02)¿10-3. The estimated imaginary part of the nonresonant component of the Love number implies a phase angle in the diurnal tidal response of the Earth of 0.7¿¿0.5¿ (lag).