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)
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