  This paper deals with an extension of our previous work [J. Phys. A: Math.
Theor. {\bf 40} F817] by considering an alternative construction of canonical
and deformed vector coherent states (VCSs) of the Gazeau-Klauder type
associated with generalized spin-orbit Hamiltonians. We define an annihilation
operator which takes into account the finite dimensional space of states
induced by the $k$-photon transition processes of the two-level atom
interacting with the single-mode radiation field. The class of nonlinear VCSs
(NVCSs) corresponding to the action of the annihilation operator is deduced and
expressed in terms of generalized displacement operators. Various NVCSs
including their "dual" counterparts are also discussed. Still by using the
Hilbert space structure, a new family of NVCSs parameterized by unit vectors of
the $S^3$ sphere has been identified without making use of the annihilation
operator.
