  We simulate Barkhausen avalanches on fractal clusters in a two-dimensional
diluted Ising ferromagnet with an effective Gaussian random field. We vary the
concentration of defect sites $c$ and find a scaling region for moderate
disorder, where the distribution of avalanche sizes has the form $D(s,c,L) =
s^{-(1+\tau (c))}{\cal{D}}(sL^{-D_s(c)})$. The exponents $\tau (c)$ for size
and $\alpha (c)$ for length distribution, and the fractal dimension of
avalanches $D_s(c)$ satisfy the scaling relation $D_s(c)\tau (c) =\alpha (c)$.
For fixed disorder the exponents vary with driving rate in agreement with
experiments on amorphous Si-Fe alloys.
