  We propose a new strategy to probe the power spectrum on large scales using
galaxy peculiar velocities. We explore the properties of surveys that cover
only two small fields in opposing directions on the sky. Surveys of this type
have several advantages over those that attempt to cover the entire sky; in
particular, by concentrating galaxies in narrow cones these surveys are able to
achieve the density needed to measure several moments of the velocity field
with only a modest number of objects, even for surveys designed to probe scales
$\gtwid 100$\hmpc. We construct mock surveys with this geometry and analyze
them in terms of the three moments to which they are most sensitive. We
calculate window functions for these moments and construct a $\chi^2$ statistic
which can be used to put constraints on the power spectrum. In order to explore
the sensitivity of these surveys, we calculate the expectation values of the
moments and their associated measurement noise as a function of the survey
parameters such as density and depth and for several popular models of
structure formation. In addition, we have studied how well these kind of
surveys can distinguish between different power spectra and found that, for the
same number of objects, cone surveys are as good or better than full-sky
surveys in distinguishing between popular cosmological models. We find that a
survey with $200-300$ galaxy peculiar velocities with distance errors of 15% in
two cones with opening angle of $\sim 10^\circ$ could put significant
constraints on the power spectrum on scales of $100-300$\hmpc, where few other
constraints exist.
