  We consider the time-dependent bi-coherent states that are essentially the
Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic
oscillator. Starting from some q-deformations of the oscillator algebra for
which the entire deformed Fock space can be constructed explicitly, we define
the q-deformed bi-coherent states. We verify the generalized Heisenberg's
uncertainty relations projected onto these states. For the initial value in
time, the states are shown to satisfy a generalized version of Heisenberg's
uncertainty relations. For the initial value in time and for the parameter of
noncommutativity $\theta =0$, the inequalities are saturated for the
simultaneous measurement of the position-momentum observables. When the time
evolves the uncertainty products are different from their values at the initial
time and do not always respect the generalized uncertainty relations.
