  We report the results of a study of $B^{\pm}\to K^{\pm}\eta_c$ and
$B^{\pm}\to K^{\pm}\eta_c(2S)$ decays followed by $\eta_c$ and $\eta_c(2S)$
decays to $(K_SK\pi)^0$. The results are obtained from a data sample containing
535 million $B\bar{B}$-meson pairs collected by the Belle experiment at the
KEKB $e^+e^-$ collider. We measure the products of the branching fractions
${\mathcal B}(B^{\pm}\to K^{\pm}\eta_c){\mathcal B}(\eta_c\to K_S
K^{\pm}\pi^{\mp})=(26.7\pm 1.4(stat)^{+2.9}_{-2.6}(syst)\pm 4.9(model))\times
10^{-6}$ and ${\mathcal B}(B^{\pm}\to K^{\pm}\eta_c(2S)){\mathcal
B}(\eta_c(2S)\to K_S
K^{\pm}\pi^{\mp})=(3.4^{+2.2}_{-1.5}(stat+model)^{+0.5}_{-0.4} syst))\times
10^{-6}$. Interference with the non-resonant component leads to significant
model uncertainty in the measurement of these product branching fractions. Our
analysis accounts for this interference and allows the model uncertainty to be
reduced. We also obtain the following charmonia masses and widths:
$M(\eta_c)=(2985.4\pm 1.5(stat)^{+0.5}_{-2.0}(syst))$ MeV/$c^2$,
$\Gamma(\eta_c)=(35.1\pm 3.1(stat)^{+1.0}_{-1.6}(syst))$ MeV/$c^2$,
$M(\eta_c(2S))=(3636.1^{+3.9}_{-4.2}(stat+model)^{+0.7}_{-2.0}(syst))$
MeV/$c^2$,
$\Gamma(\eta_c(2S))=(6.6^{+8.4}_{-5.1}(stat+model)^{+2.6}_{-0.9}(syst))$
MeV/$c^2$.
