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We present a search for new planetary-mass members of nearby young movinggroups (YMGs) using astrometry for 694 T and Y dwarfs, including 447 objectswith parallaxes, mostly produced by recent large parallax programs from UKIRTand Spitzer. Using the BANYAN $\Sigma$ and LACEwING algorithms, we identify 30new candidate YMG members, with spectral types of T0$-$T9 and distances of$10-43$ pc. Some candidates have unusually red colors and/or faint absolutemagnitudes compared to field dwarfs with similar spectral types, providingsupporting evidence for their youth, including 4 early-T dwarfs. We establishone of these, the variable T1.5 dwarf 2MASS J21392676$+$0220226, as a newplanetary-mass member ($14.6^{+3.2}_{-1.6}$ M$_{\rm Jup}$) of the Carina-Neargroup ($200\pm50$ Myr) based on its full six-dimensional kinematics, includinga new parallax measurement from CFHT. The high-amplitude variability of thisobject is suggestive of a young age, given the coexistence of variability andyouth seen in previously known YMG T dwarfs. Our four latest-type (T8$-$T9) YMGcandidates, WISE J031624.35$+$430709.1, ULAS J130217.21$+$130851.2, WISEPCJ225540.74$-$311841.8, and WISE J233226.49$-$432510.6, if confirmed, will bethe first free-floating planets ($\approx2-6$ M$_{\rm Jup}$) whose ages andluminosities are compatible with both hot-start and cold-start evolutionarymodels, and thus overlap the properties of the directly-imaged planet 51 Eri b.Several of our early/mid-T candidates have peculiar near-infrared spectra,indicative of heterogenous photospheres or unresolved binarity. Radial velocitymeasurements needed for final membership assessment for most of our candidatesawait upcoming 20$-$30 meter class telescopes. In addition, we compile all 15known T7$-$Y1 benchmarks and derive a homogeneous set of their effectivetemperatures, surface gravities, radii, and masses.

The Hawaii Infrared Parallax Program. V. New T-Dwarf Members and Candidate Members of Nearby Young Moving Groups