  We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic
method. We apply the Schr\"odinger factorization to the radial Hamiltonian of
the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy
spectrum is found by using the theory of unitary irreducible representations.
By solving analytically the Schr\"odinger equation, we construct the Sturmian
basis for the unitary irreducible representations of the $su(1,1)$ Lie algebra.
We construct the $SU(1,1)$ Perelomov radial coherent states for this problem
and compute their time evolution.
