  (Abridged) To investigate the black hole mass (MBH) vs. stellar velocity
dispersion relation of active galaxies, we measured the velocity dispersions of
a sample of local Seyfert 1 galaxies, for which we have recently determined MBH
using reverberation mapping. For most objects, velocity dispersions were
measured from high S/N ratio optical spectra centered on the Ca II triplet
region (~8500 A), obtained at the Keck, Palomar, and Lick Observatories. For
two objects, in which the Ca II triplet region was contaminated by nuclear
emission, the measurement was based on high-quality H-band spectra obtained
with the OSIRIS at the Keck-II Telescope. Combining our new measurements with
data from the literature, we assemble a sample of 24 active galaxies with
stellar velocity dispersions and reverberation-based MBH measurements in the
range of black hole mass 10^6<MBH/M_sun<10^9. We use this sample to obtain
reverberation mapping constraints on the slope and intrinsic scatter of the
M-sigma relation of active galaxies. Assuming a constant virial coefficient f
for the reverberation mapping black hole masses, we find a slope b=3.55+-0.60
and the intrinsic scatter sigma_int=0.43+-0.08 dex in the relation log
(MBH/M_sun) = a + b log (sigma/200 km/s), which are consistent with those found
for quiescent galaxies. We derive an updated value of the virial coefficient f
by finding the value which places the reverberation masses in best agreement
with the M-sigma relation of quiescent galaxies; using the quiescent M-sigma
relation determined by Gultekin et al. we find log f=0.72^{+0.09-0.10} with an
intrinsic scatter of 0.44+-0.07 dex. The uncertainty of the virial coefficient
remains one of the main sources of the uncertainty in black hole mass
determinations using reverberation mapping, and therefore also in single-epoch
spectroscopic estimates of MBH in active galaxies.
