In this paper we construct the Lagrangian and Hamiltonian formulations of N=4 supersymmetric systems describing the motion of an isospin particle on a conformally flat four-manifold with SO(4) isometry carrying the non-Abelian field of a Belavin-Polyakov-Shvarts-Tyupkin instanton. The conformal factor can be specified to yield various particular systems, such as superconformally invariant mechanics as well as a particle on the four-sphere, the pseudosphere, or on R×S3. The isospin degrees of freedom arise as bosonic components of an additional fermionic N=4 supermultiplet, whose other components are rendered auxiliary by a nonlocal redefinition. Our on-shell component action coincides with the one recently proposed in [arXiv:0912.3289].