  The first dedicated search for the $\eta_{c2}(1D)$ is carried out using the
decays $B^+ \rightarrow \eta_{c2}(1D) K^+$, $B^0 \rightarrow \eta_{c2}(1D)
K^0_S$, $B^0 \rightarrow \eta_{c2}(1D) \pi^- K^+$, and $B^+ \rightarrow
\eta_{c2}(1D) \pi^+ K^0_S$ with $\eta_{c2}(1D) \to h_c \gamma$. No significant
signal is found. For the $\eta_{c2}(1D)$ mass range between $3795$ and $3845\
\mathrm{MeV}/c^2$, the branching-fraction upper limits are determined to be
$\mathcal{B}(B^+ \rightarrow \eta_{c2}(1D) K^+) \times
\mathcal{B}(\eta_{c2}(1D) \to h_c \gamma) < 3.7 \times 10^{-5}$,
$\mathcal{B}(B^0 \rightarrow \eta_{c2}(1D) K^0_S) \times
\mathcal{B}(\eta_{c2}(1D) \to h_c \gamma) < 3.5 \times 10^{-5}$,
$\mathcal{B}(B^0 \rightarrow \eta_{c2}(1D) \pi^- K^+) \times
\mathcal{B}(\eta_{c2}(1D) \to h_c \gamma) < 1.0 \times 10^{-4}$, and
$\mathcal{B}(B^+ \rightarrow \eta_{c2}(1D) \pi^+ K^0_S) \times
\mathcal{B}(\eta_{c2}(1D) \to h_c \gamma) < 1.1 \times 10^{-4}$ at 90% C. L.
The analysis is based on the 711 $\mathrm{fb}^{-1}$ data sample collected on
the $\Upsilon(4S)$ resonance by the Belle detector, which operated at the KEKB
asymmetric-energy $e^+ e^-$ collider.
