The interpretation of teleseismic receiver functions (RFs) is typically limited by poor constraints on the uncertainty of amplitudes of converted phases. In continental regions these problems are overcome by stacking large amounts of data. In oceanic regions, however, data quality is notoriously noisy and the number of events are often limited by significantly shorter station deployment times. Estimates of RF pulse amplitude uncertainty are, therefore, necessary to allow an analyst to differentiate between real structure in the Earth and random correlations in ambient noise. Here we combine a common-conversion-point stacking technique with multiple-taper correlation RF estimates, which allow frequency-domain weighting. We then compute jackknife statistics to estimate local uncertainties in RF amplitude. We apply this technique to a continental station in Arabia (RAYN) and to the ocean island station at Raratonga, Cook Islands (RAR) in order to compare our method to results obtained via other techniques. The structure we recover matches previous crustal studies at both stations and provides new interpretations of conversions in the upper mantle. At single stations this technique works well to resolve crust and mantle structure up to a depth of 100 km. Geographical dispersion of ray paths at greater depths decreases the number of events per bin and, therefore, increases the uncertainty in converted amplitude. The ability to stack crossing ray paths implies that this method will be well suited to the analysis of data from seismic arrays.