  Supernova (SN) rates are a potentially powerful diagnostic of star formation
history (SFH), metal enrichment, and SN physics, particularly in galaxy
clusters with their deep, metal-retaining potentials, and simple SFH. However,
a low-redshift cluster SN rate has never been published. We derive the SN rate
in galaxy clusters at 0.06<z<0.19, based on type Ia supernovae (SNe Ia) that
were discovered by the Wise Observatory Optical Transient Survey. As described
in a separate paper, a sample of 140 rich Abell clusters was monitored, in
which six cluster SNe Ia were found and confirmed spectroscopically. Here, we
determine the SN detection efficiencies of the individual survey images, and
combine the efficiencies with the known spectral properties of SNe Ia to
calculate the effective visibility time of the survey. The cluster stellar
luminosities are measured from the Sloan Digital Sky Survey (SDSS) database in
the griz SDSS bands. Uncertainties are estimated using Monte-Carlo simulations
in which all input parameters are allowed to vary over their known
distributions. We derive SN rates normalized by stellar luminosity, in SNU
units (SNe per century per 10^10 L_sun) in five photometric bandpasses, of
0.36+/-(0.22,0.14)+/-0.02 (B), 0.351+/-(0.210,0.139)+/-0.020 (g),
0.288+/-(0.172,0.114)+/-0.018 (r), 0.229+/-(0.137,0.091)+/-0.014 (i),
0.186+/-(0.111,0.074)+/-0.010 (z), where the quoted errors are statistical and
systematic, respectively. The SN rate per stellar mass unit, derived using a
color-luminosity-mass relation, is 0.098+/-(0.059,0.039)+/-0.009 SNe (century
10^10 M_sun)^-1. The low cluster SN rates we find are similar to, and
consistent with, the SN Ia rate in local elliptical galaxies.
