  We present a high-precision infrared radial velocity study of late-type stars
using spectra obtained with NIRSPEC at the W. M. Keck Observatory. Radial
velocity precisions of 50 m/s are achieved for old field mid-M dwarfs using
telluric features for precise wavelength calibration. Using this technique, 20
young stars in the {\beta} Pic (age ~12 Myr) and TW Hya (age ~8 Myr)
Associations were monitored over several years to search for low mass
companions; we also included the chromospherically active field star GJ 873 (EV
Lac) in this survey. Based on comparisons with previous optical observations of
these young active stars, radial velocity measurements at infrared wavelengths
mitigate the radial velocity noise caused by star spots by a factor of ~3.
Nevertheless, star spot noise is still the dominant source of measurement error
for young stars at 2.3 {\mu}m, and limits the precision to ~77 m/s for the
slowest rotating stars (v sin i < 6 km/s), increasing to ~168 m/s for rapidly
rotating stars (v sin i > 12 km/s). The observations reveal both GJ 3305 and
TWA 23 to be single-lined spectroscopic binaries; in the case of GJ 3305, the
motion is likely caused by its 0.09" companion, identified after this survey
began. The large amplitude, short-timescale variations of TWA 13A are
indicative of a hot Jupiter-like companion, but the available data are
insufficient to confirm this. We label it as a candidate radial velocity
variable. For the remainder of the sample, these observations exclude the
presence of any 'hot' (P < 3 days) companions more massive than 8 MJup, and any
'warm' (P < 30 days) companions more massive than 17 MJup, on average. Assuming
an edge-on orbit for the edge-on disk system AU Mic, these observations exclude
the presence of any hot Jupiters more massive than 1.8 MJup or warm Jupiters
more massive than 3.9 MJup.
