Manipulating thermal transport by designing materials with control of their properties over the entire spectral range of vibrational frequencies would provide a unique path to create solids with designer thermal conductivities. Traditional routes of nanostructuring to reduce the vibrational thermal conductivity of solids typically target narrow bands of the vibrational energy spectrum, which is often based on the characteristic dimensions of the nanostructure. In this work, we demonstrate the ability to simultaneously impact the phonon transport of both high- and low-frequency modes by creating defects that act as both high-frequency phonon scattering sites while coherently manipulating low-frequency waves via resonance with the long wavelength phonons. We use atomistic simulations to identify fullerenes functionalized on the sidewalls of carbon nanotubes (CNT) as efficient phonon blocks realized through localized resonances that appear due to hybridization between the modes of the fullerene and the underlying CNT. We show that with a large surface coverage and high periodicity in the inclusion of the covalently bonded fullerenes, the thermal conductivity of individual CNTs can be lowered by more than an order of magnitude, thus providing a large tunability in the thermal transport across these materials. We prescribe the large reduction in thermal conductivity to a combination of resonant phonon localization effects leading to phonon band anticrossings and vibrational scattering effects due to the inclusion of the strongly bonded fullerene molecules.