  We present new MMT/Hectochelle spectroscopic measurements for 257 stars
observed along the line of sight to the ultra-faint dwarf galaxy Triangulum II.
Combining with results from previous Keck/DEIMOS spectroscopy, we obtain a
sample that includes 16 likely members of Triangulum II, with up to 10
independent redshift measurements per star. To this multi-epoch kinematic data
set we apply methodology that we develop in order to infer binary orbital
parameters from sparsely sampled radial velocity curves with as few as two
epochs. For a previously-identified (spatially unresolved) binary system in
Tri~II, we infer an orbital solution with period $296.0_{-3.3}^{+3.8} \rm~
days$ , semi-major axis $1.12^{+0.41}_{-0.24}\rm~AU$, and a systemic velocity $
-380.0 \pm 1.7 \rm~km ~s^{-1}$ that we then use in the analysis of Tri~II's
internal kinematics. Despite this improvement in the modeling of binary star
systems, the current data remain insufficient to resolve the velocity
dispersion of Triangulum II. We instead find a 95% confidence upper limit of
$\sigma_{v} \lesssim 3.4 \rm ~km~s^{-1}$.
