  We model the number of detectable supernovae (SNe) as a function of redshift
at different flux thresholds, making use of the observed properties of local
SNe, such as their lightcurves, fiducial spectra, and peak magnitude
distributions. We obtain a rate of 0.4-2.3 SNe/arcmin^2/yr at z > 5 at the near
infrared (4.5 micron) flux density threshold of 3 nJy (achievable with the
James Webb Space Telescope (JWST) in a 10^5 s integration). In a hypothetical
one-year survey, it should be possible to detect up to several thousand SNe per
unit redshift at z > 6. We discuss the possible application of such a large
sample of distant SNe as a probe of the epoch of reionization. By heating the
intergalactic medium and raising the cosmological Jeans mass, the process of
reionization can suppress star formation in low-mass galaxies. This could have
produced a relatively sharp drop in the SNR around the redshift of
reionization. We quantify the detectability of this feature in future surveys
of distant SNe by varying the redshift and duration of the feature, as well as
its impact on the SFR in low-mass halos, which results in different redshifts,
widths, and sizes of the drop in the expected SFR. We find that the drop can be
detected out to z_re ~ 13, as long as (i) the reionization history contains a
relatively rapid feature which is synchronized over different regions to within
\Delta z < 1 - 3, (ii) the star-formation efficiency in halos that dominate
reionization is ~ 10%, and (iii) reionization significantly suppresses the star
formation in low-mass halos. Depending on the details of (i) - (iii), this
could be achieved with a survey lasting less than two weeks. Detecting this
signature would also help elucidate the feedback mechanism that regulates
reionization.
