  In this work we study and exactly solve the Dirac oscillator with three
different topological defects, namely the cosmic string spacetime
($\Lambda_\mp$), the magnetic cosmic string spacetime ($\Theta_\mp$) and the
cosmic dislocation spacetime ($\Pi_\mp$). Moreover, we show that the radial
part of this problem possess an $SU(1,1)$ symmetry. From this, we obtain the
wave functions and their respective energy spectrum by means of the
Schr\"odinger factorization. Also, we compute the radial coherent states of the
eigenfunctions of each problem and their time evolution.
