  We report kelvin to millikelvin-temperature measurements of dissipation and
frequency shift in megahertz-range resonators fabricated from
ultra-nanocrystalline diamond. Frequency shift $\delta f/f_0$ and dissipation
$Q^{-1}$ demonstrate temperature dependence in the millikelvin range similar to
that predicted by the glass model of tunneling two level systems. The
logarithmic temperature dependence of $\delta f/ f_0$ is in good agreement with
such models, which include phonon relaxation and phonon resonant absorption.
Dissipation shows a weak power law, $Q^{-1}\propto T^{{1/3}}$, followed by
saturation at low temperature. A comparison of both the scaled frequency shift
and dissipation in equivalent micromechanical structures made of single-crystal
silicon and gallium arsenide indicates universality in the dynamical response.
