  We present magnetization measurements for the upper critical field $H_{c2}$
on aligned Na$_{x}$(H$_{3}$O)$_{z}$CoO$_{2}\cdot y$H$_{2}$O superconductors
with magnetic field parallel to CoO$_2$ layers. The temperature-dependent part
of the normal-state magnetization $M(H,T)$ can be well scaled with Brillouin
function, suggesting the existence of impurity moments. By subtracting the
contribution of the magnetic impurity moments, a well defined onset of
superconducting diamagnetism allows the in-field superconducting transition
temperature $T_{c}$($H$) accurately determined. No superconducting transition
was observed down to 1.9 K under an applied field of 8 Tesla. The result
suggests that the $H^{\|ab}_{c2}(0)$ value is just within the Pauli
paramagnetic limit, supporting spin-singlet superconductivity in the cobalt
oxyhydrate superconductor. Additionally, the upward curvature near $T_{c}$ in
the $H^{\|ab}_{c2}-T$ phase diagram was confirmed to be intrinsic. Possible
origin of the anomaly was discussed.
