  We give a \theta-deformed version of the ADHM construction of SU(2)
instantons with arbitrary topological charge on the sphere S^4. Classically the
instanton gauge fields are constructed from suitable monad data; we show that
in the deformed case the set of monads is itself a noncommutative space. We use
these monads to construct noncommutative `families' of SU(2) instantons on the
deformed sphere S^4_\theta. We also compute the topological charge of each of
the families. Finally we discuss what it means for such families to be gauge
equivalent.
