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 $D(s,c,L) = s^{-(1+��(c))}{\cal{D}}(sL^{-D_s(c)})$. The exponents $��(c)$ for size and $��(c)$ for length distribution, and the fractal dimension of avalanches $D_s(c)$ satisfy the scaling relation $D_s(c)��(c) =��(c)$. For fixed disorder the exponents vary with driving rate in agreement with experiments on amorphous Si-Fe alloys.

5 pages, Latex, 4 PostScript figures included