  We present a detailed orbital and stability analysis of the HD~59686
binary-star planet system. HD~59686 is a single-lined moderately close ($a_{B}
= 13.6\,$AU) eccentric ($e_{B} = 0.73$) binary, where the primary is an evolved
K giant with mass $M = 1.9 M_{\odot}$ and the secondary is a star with a
minimum mass of $m_{B} = 0.53 M_{\odot}$. Additionally, on the basis of precise
radial velocity (RV) data a Jovian planet with a minimum mass of $m_p = 7
M_{\mathrm{Jup}}$, orbiting the primary on a nearly circular S-type orbit with
$e_p = 0.05$ and $a_p = 1.09\,$AU, has recently been announced. We investigate
large sets of orbital fits consistent with HD 59686's radial velocity data by
applying bootstrap and systematic grid-search techniques coupled with
self-consistent dynamical fitting. We perform long-term dynamical integrations
of these fits to constrain the permitted orbital configurations. We find that
if the binary and the planet in this system have prograde and aligned coplanar
orbits, there are narrow regions of stable orbital solutions locked in a
secular apsidal alignment with the angle between the periapses, $\Delta
\omega$, librating about $0^\circ$. We also test a large number of mutually
inclined dynamical models in an attempt to constrain the three-dimensional
orbital architecture. We find that for nearly coplanar and retrograde orbits
with mutual inclination $145^\circ \lesssim \Delta i \leq 180^\circ$, the
system is fully stable for a large range of orbital solutions.
