  Nonlinear `sigma' models in two dimensions have BPS solitons which are
solutions of self- and anti-self-duality constraints. In this paper, we find
their analogues for fuzzy sigma models on fuzzy spheres which were treated in
detail by us in earlier work. We show that fuzzy BPS solitons are quantized
versions of `Bott projectors', and construct them explicitly. Their
supersymmetric versions follow from the work of S. Kurkcuoglu.
