  Powerful gravitational telescopes in the form of massive galaxy clusters can
be used to enhance the light collecting power over a limited field of view by
about an order of magnitude in flux. This effect is exploited here to increase
the depth of a survey for lensed supernovae at near-IR wavelengths. A pilot SN
search program conducted with the ISAAC camera at VLT is presented. Lensed
galaxies behind the massive clusters A1689, A1835 and AC114 were observed for a
total of 20 hours split into 2, 3 and 4 epochs respectively, separated by
approximately one month to a limiting magnitude J<24 (Vega). Image subtractions
including another 20 hours worth of archival ISAAC/VLT data were used to search
for transients with lightcurve properties consistent with redshifted
supernovae, both in the new and reference data. The feasibility of finding
lensed supernovae in our survey was investigated using synthetic lightcurves of
supernovae and several models of the volumetric Type Ia and core-collapse
supernova rates as a function of redshift. We also estimate the number of
supernova discoveries expected from the inferred star formation rate in the
observed galaxies. The methods consistently predict a Poisson mean value for
the expected number of SNe in the survey between N_SN=0.8 and 1.6 for all
supernova types, evenly distributed between core collapse and Type Ia SN. One
transient object was found behind A1689, 0.5" from a galaxy with photometric
redshift z_gal=0.6 +- 0.15. The lightcurve and colors of the transient are
consistent with being a reddened Type IIP SN at z_SN=0.59. The lensing model
predicts 1.4 magnitudes of magnification at the location of the transient,
without which this object would not have been detected in the near-IR ground
based search described in this paper (unlensed magnitude J~25). (abridged)
