  We propose a scheme that combines velocity-selective coherent population
trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of
optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on
an inverted $\mathsf{Y}$ configuration in an alkali-metal atom. It consists of
a $\Lambda$ formed by two Raman transitions between the ground hyperfine levels
and the $D$ transition, allowing RSC along two paths and formation of a CPT
dark state. Using state-dependent difference in vibration frequency of the atom
in a circularly polarized trap, we can tune the $\Lambda$ to make only the
motional ground state a CPT dark state. We call this scheme motion-selective
coherent population trapping (MSCPT). We write the master equations for RSC and
MSCPT and solve them numerically for a $^{87}$Rb atom in a one-dimensional
optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the
steady state slowly compared with RSC, the former consistently produces colder
atoms than the latter. The numerical results also show that subrecoil cooling
by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet
experimentally feasible, condition. We explain this performance quantitatively
by calculating the relative darkness of each motional state. Finally, we
discuss on application of the MSCPT scheme to an optically trapped diatomic
polar molecule whose Stark shift and vibration frequency exhibit large
variations depending on the rotational quantum number.
