  (ABRIDGED) We have performed the first detailed spectral analysis of red
giant members of the relatively high-metallicity globular cluster (GC)
Tononzintla~2 (Ton~2) using high-resolution near-infrared spectra collected
with the Apache Point Observatory Galactic Evolution Experiment II survey
(APOGEE-2), obtained as part of the bulge Cluster APOgee Survey. We investigate
chemical abundances for a variety of species including the light-, odd-Z,
$\alpha$-, Fe-peak, and neutron-capture elements from high S/N spectra of seven
giant members. The derived mean cluster metallicity is [Fe/H]$=-0.70\pm0.05$,
with no evidence for an intrinsic metallicity spread. Ton~2 exhibits a typical
$\alpha$-enrichment that follows the trend for high-metallicity Galactic GCs,
similar to that seen in 47~Tucanae and NGC~6380. We find a significant nitrogen
spread ($>0.87$ dex), and a large fraction of nitrogen-enriched stars that
populate the cluster. Given the relatively high-metallicity of Ton~2, these
nitrogen-enriched stars are well above the typical Galactic levels, indicating
the prevalence of the multiple-population phenomenon in this cluster which also
contains several stars with typical low, first-generation N abundances. We also
identify the presence of [Ce/Fe] abundance spread in Ton~2, which is correlated
with the nitrogen enhancement, indicating that the \textit{s}-process
enrichment in this cluster has been produced likely by relatively low-mass
Asymptotic Giant Branch stars. Furthermore, we find a mean radial velocity of
the cluster, $-178.6\pm0.86$ km s$^{-1}$ with a small velocity dispersion,
2.99$\pm$0.61 km s$^{-1}$, which is typical of a GC. We also find a prograde
bulge-like orbit for Ton~2 that appears to be radial and highly eccentric.
