  We present a systematic single-dish search for molecular outflows toward a
sample of 9 candidate low-luminosity protostars and 30 candidate Very Low
Luminosity Objects (VeLLOs; L_int < 0.1 L_sun). The sources are identified
using data from the Spitzer Space Telescope catalogued by Dunham et al. toward
nearby (D < 400 pc) star forming regions. Each object was observed in 12CO and
13CO J = 2-1 simultaneously using the sideband separating ALMA Band-6 prototype
receiver on the Heinrich Hertz Telescope at 30 arcsecond resolution. Using
5-point grid maps we identify five new potential outflow candidates and make
on-the-fly maps of the regions surrounding sources in the dense cores B59,
L1148, L1228, and L1165. Of these new outflow candidates, only the map of B59
shows a candidate blue outflow lobe associated with a source in our survey. We
also present larger and more sensitive maps of the previously detected L673-7
and the L1251-A IRS4 outflows and analyze their properties in comparison to
other outflows from VeLLOs. The accretion luminosities derived from the outflow
properties of the VeLLOs with detected CO outflows are higher than the observed
internal luminosity of the protostars, indicating that these sources likely had
higher accretion rates in the past. The known L1251-A IRS3 outflow is detected
but not remapped. We do not detect clear, unconfused signatures of red and blue
molecular wings toward the other 31 sources in the survey indicating that
large-scale, distinct outflows are rare toward this sample of candidate
protostars. Several potential outflows are confused with kinematic structure in
the surrounding core and cloud. Interferometric imaging is needed to
disentangle large-scale molecular cloud kinematics from these potentially weak
protostellar outflows.
