  Ultra-light dark matter perturbs the orbital motion of binary pulsars, in
particular by causing peculiar time variations of a binary's orbital
parameters, which then induce variations in the pulses' times-of-arrival.
Binary pulsars have therefore been shown to be promising detectors of
ultra-light dark matter. To date, the sensitivity of binary pulsars to
ultra-light dark matter has only been studied for dark matter masses in a
narrow resonance band around a multiple of the binary pulsar orbital frequency.
In this study we devise a two-step, bayesian method that enables us to compute
semi-analytically the sensitivity for all masses, also away from the resonance,
and to combine several observed binaries into one global sensitivity curve. We
then apply our method to the case of a universal, linearly-coupled, scalar
ultra-light dark matter. We find that with next-generation radio observatories
the sensitivity to the ultra-light dark matter coupling will surpass that of
solar-system constraints for a decade in mass around $m\sim10^{-21}$
$\text{eV}$, even beyond resonance.
