  In this article we investigate and solve exactly the modified Dirac
oscillator in curved spacetime with spin and pseudospin symmetries through an
algebraic approach. By focusing on the radial part of this problem, we use the
Schr\"odinger factorization method to show that this problem possesses an SU(1;
1) symmetry. This symmetry allowed us to obtain the wave functions and their
corresponding energy spectrum. From these results, we calculate the radial
coherent states of the modified Dirac oscillator and their temporal evolution
in the spin and pseudospin limits, respectively.
