Come to think of it I`ve never heard the term "dipole motion" before. The term dipole typically refers to one of two things (I had assumed that person meant two bodies orbiting each other).

(1) Electric Dipole - the product of the distance between the two poles (as magnetic or electric) of a dipole and the magnitude of either pole

(2) Dipole term in multipole expansion - The mathematical expression for a potential can usually be expanded in a multipole expansion.

The later has the form phi = "1/r term" + "dipole term" + "quadrupole term" + .....

The dipole term is an integral of a term like x*rho where rho is the mass density. For two point charges of opposite sign this gives a non-zero term. However if the charges are of the same sign the term can be made to vanish (given the right coordinate system). If the potential isn`t electric but gravitational then there is only one sign to the "gravitational charge" and thus will make the dipole term vanish. The quadropole moment doesn`t vanish. It contributes to the gravitational waves.