  Amplitude methods have proven to be a promising technique to perform
Post-Minkowskian calculations used as inputs to construct gravitational
waveforms. In this paper, we show how these methods can be extended beyond the
standard calculations in General Relativity with a minimal coupling to matter.
As proof of principle, we consider spinless particles conformally coupled to a
gravitational helicity-0 mode. We clarify the subtleties in the matching
procedure that lead to the potential for conformally coupled matter. We show
that in the probe particle limit, we can reproduce well known results for the
field profile. With the scattering amplitudes at hand, we compute the
conservative potential and scattering angle for the binary system. We find that
the result is a non trivial expansion that involves not only the coupling
strengths, but also a non trivial dependence on the energy/momentum of the
scattered particles.
