  Basic idea presented in Parts (I) and (II) for the deformed boson scheme is
applied to the case of the su(2,1)-algebra for describing many-body systems
consisting of three kinds of boson operators. A possible form of the coherent
state for the su(2,1)-algebra is generalized and the deformed su(2,1)-algebra
is presented. As an application, the time-evolution of the statistically mixed
state in a certain boson system, which has been already investigated by the
present authors, is reinvestigated.
