We have used moderate resolution, near-infrared spectra from the SpeX spectrograph on the NASA Infrared Telescope facility to characterize the stellar content of Barnard 59 (B59), the most active star-forming core in the Pipe Nebula. Measuring luminosity and temperature sensitive features in the spectra of 20 candidate YSOs, we identified likely background giant stars and measured each stars spectral type, extinction, and NIR continuum excess. We find that B59 is composed of late type (K4-M6) low-mass (0.9--0.1 M_sun) YSOs whose median stellar age is comparable to, if not slightly older than, that of YSOs within the Rho Oph, Taurus, and Chameleon star forming regions. Deriving absolute age estimates from pre-main sequence models computed by DAntona et al., and accounting only for statistical uncertainties, we measure B59s median stellar age to be 2.6+/-0.8 Myrs. Including potential systematic effects increases the error budget for B59s median (DM98) stellar age to 2.6+4.1/-2.6 Myrs. We also find that the relative age orderings implied by pre-main sequence evolutionary tracks depend on the range of stellar masses sampled, as model isochrones possess significantly different mass dependencies. The maximum likelihood median stellar age we measure for B59, and the regions observed gas properties, suggest that the B59 dense core has been stable against global collapse for roughly 6 dynamical timescales, and is actively forming stars with a star formation efficiency per dynamical time of ~6%. This maximum likelihood value agrees well with recent star formation simulations that incorporate various forms of support against collapse, such as sub-critical magnetic fields, outflows, and radiative feedback from protostellar heating. [abridged]
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