  We explore mechanisms of interferences under which the spin-independent
interaction in the scattering of scalar dark matter with nucleus is suppressed.
We offer a detailed derivation of the nuclear amplitudes based on the
interactions with quarks in the framework of a nonuniversal $U(1)'$ extension
of the standard model. By assuming a range of parameters compatible with
collider searches, electroweak observables and dark matter abundance, we find
scenarios for destructive interferences with and without isospin symmetry. The
model reveals solutions with mutually interfering scalar particles, canceling
the effective spin-independent coupling with only scalar interactions, which
requires an extra Higgs boson with mass $M_{H}>125$ GeV. The model also
possesses scenarios with only vector interactions through two neutral gauge
bosons, $Z$ and $Z'$. Due to the nonuniversality of the $U(1)'$ symmetry, we
distinguish two family structures of the quark sector with different numerical
predictions. In one case, we obtain cross sections that pass all the
Xenon-based detector experiments. In the other case, limits from LUX experiment
enclose an exclusion region for dark matter between $9$ and $800$ GeV. We
examine a third scenario with isospin-violating couplings where interferences
between scalar and vector boson exchanges cancel the scattering. We provide
solutions where interactions with Xenon-based detectors is suppressed for light
dark matter, below $6$ GeV, while interactions with Germanium- and
Silicon-based detectors exhibit solutions up to the regions of interest for
positive signals reported by CoGeNT and CDMS-Si experiments, and compatible
with the observed DM relic density for DM mass in the range $8.3-10$ GeV.
Spin-dependent interactions become the dominant source of scattering around the
interference regions, where Maxwellian speed distribution is considered.
