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~IIs 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 $sigma_{v} lesssim 3.4 rm ~km~s^{-1}$.
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