We present and apply an approximate general theory for the effects of the direct interactions on the translational and rotational diffusion coefficients of a nonspherical Brownian particle interacting with other spherical particles diffusing around it. These results are specialized to a system formed by a charged axially-symmetric macroparticle that diffuses in an ionic solution, whose static properties are described within the Debye-Huckel approximation. In particular, we calculate the static friction coefficients of a Brownian point-dipole embedded in a hard-sphere, and of a charged hard-ellipsoidal tracer particle.