  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 star's 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 D'Antona et
al., and accounting only for statistical uncertainties, we measure B59's median
stellar age to be 2.6+/-0.8 Myrs. Including potential systematic effects
increases the error budget for B59's 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 region's 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]
