  Interpreting the coordinates of the quantum Euclidean space R_q^4 [the
SO_q(4)-covariant noncommutative space] as the entries of a ``q-quaternion
matrix'' we construct (anti)instanton solutions of a would-be q-deformed su(2)
Yang-Mills theory on R_q^4. Since the (anti)selfduality equations are covariant
under the quantum group of deformed rotations, translations and scale change,
by applying the latter we can respectively generate ``gauge equivalent'' or
``inequivalent'' solutions from the one centered at the origin and with unit
size. We also construct multi-instanton solutions. As these solutions depend on
noncommuting parameters playing the roles of `sizes' and `coordinates of the
centers' of the instantons, this indicates that the moduli space of a complete
theory should be a noncommutative manifold. Similarly, as the (global) gauge
transformations relating ``gauge equivalent'' solutions depend on the
generators of two copies of SU_q(2), this suggests that gauge transformations
should be allowed to depend on additional noncommutative parameters.
