We report on a search for significant oscillations in different coronal structures by applying a wavelet analysis to Solar and Heliospheric Observatory UVCS observations of the hydrogen Lyα 1216 Å line intensity taken between 1.5 and 2.2 Rsolar. Significant periodic oscillations, unlikely to be a result of instrumental effects, are shown to exist in a coronal hole, the quiet Sun, and a streamer. Observations made sequentially at different heights but at the same latitude often share similar power spectra. Neighboring pixels at the same radial distance also share similar power spectra. These results indicate both a localized structure to the periodicity and a long-range preservation of oscillation patterns in the radial expansion of the solar wind. We show that a preference for significant oscillations with periods of 7-8 minutes exists in three out of the four observations presented here. Other bands of preferred periodicity are observed at different heights.