  The quantum field-theoretic approach to classical observables due to Kosower,
Maybee and O'Connell provides a rigorous pathway from on-shell scattering
amplitudes to classical perturbation theory. In this paper, we promote this
formalism to describe general classical spinning objects by using coherent spin
states. Our approach is fully covariant with respect to the massive little
group ${\rm SU}(2)$ and is therefore completely synergistic with the massive
spinor-helicity formalism. We apply this approach to classical two-body
scattering due gravitational interaction. Starting from the coherent-spin
elastic-scattering amplitude, we derive the classical impulse and spin kick
observables to first post-Minkowskian order but to all orders in the angular
momenta of the massive spinning objects. From the same amplitude, we also
extract an effective two-body Hamiltonian, which can be used beyond the
scattering setting. As a cross-check, we rederive the classical observables in
the center-of-mass frame by integrating the Hamiltonian equations of motion to
the leading order in Newton's constant.
