  The first search for $Z_{c}$ pair production in $\Upsilon(1S)$ and
$\Upsilon(2S)$ decays and in $e^{+}e^{-}$ annihilation at $\sqrt{s}$ = 10.52,
10.58, and 10.867 GeV is conducted using data collected with the Belle detector
at the KEKB asymmetric energy electron-positron collider. No significant
signals are observed in any of the studied modes, and the 90\% credibility
level upper limits on their product branching fractions in $\Upsilon(1S)$ and
$\Upsilon(2S)$ decays (${\cal B}(\Upsilon(1S,2S)\to Z^{+}_{c}Z^{(\prime)
-}_{c})\times{\cal B}(Z^{+}_{c}\to\pi^{+}+c\bar c)$ ($c\bar c=J/\psi$,
$\chi_{c1}(1P)$, $\psi(2S)$)) and the product of Born cross section and
branching fraction for $e^{+}e^{-} \to Z^{+}_{c}Z^{(\prime) -}_{c}$
($\sigma(e^+e^- \to Z^{+}_{c}Z^{(\prime) -}_{c})\times {\cal B}(Z^{+}_{c} \to
\pi^+ +c\bar c)$) at $\sqrt{s}$ = 10.52, 10.58, and 10.867 GeV are determined.
Here, $Z_{c}$ refers to the $Z_{c}(3900)$ and $Z_{c}(4200)$ observed in the
$\pi J/\psi$ final state, the $Z_{c1}(4050)$ and $Z_{c2}(4250)$ in the
$\pi\chi_{c1}(1P)$ state, and the $Z_{c}(4050)$ and $Z_{c}(4430)$ in the
$\pi\psi(2S)$ state.
