Context: Massive galaxy clusters at intermediate redshift can magnify the flux of distant background sources by several magnitudes. Aims: We exploit this effect to search for lensed distant supernovae that may otherwise be too faint to be detected. Methods: A supernova search was conducted at near infrared wavelengths using the ISAAC instrument at the VLT. The massive galaxy clusters Abell 1689, Abell 1835, and AC114 were observed for a total of 20 h to search for supernovae in gravitationally magnified background galaxies. The observations were split into individual epochs of 2 h of exposure time, separated by approximately one month. Image-subtraction techniques were used to search for transient objects with light curve properties consistent with supernovae, both in our new and archival ISAAC/VLT data. The limiting magnitude of the individual epochs was estimated by adding artificial stars to the subtracted images. Most of the epochs reach 90% detection efficiency at SZ(J) ≃ 23.8-24.0 mag (Vega). Results: Two transient objects, both in archival images of Abell 1689 and AC114, were detected. The transient in AC114 coincides - within the position uncertainty - with an X-ray source and is likely to be a variable AGN at the cluster redshift. The transient in Abell 1689 was found at SZ = 23.24 mag, ~0.5''away from a galaxy with photometric redshift z_gal = 0.6 ± 0.15. The light curves and the colors of the transient are consistent with a reddened type IIP supernova at redshift z = 0.59 ± 0.05. The lensing model of Abell 1689 predicts ~1.4 mag of magnification at the position of the transient, making it the most magnified supernova ever found and only the second supernova found behind a galaxy cluster. Conclusions: Our pilot survey has demonstrated the feasibility to find distant gravitationally magnified supernovae behind massive galaxy clusters. One likely supernova was found behind Abell 1689, in accordance with the expectations for this survey, as shown in an accompanying analysis paper. Based on observations made with ESO telescopes at the Paranal Observatory under program IDs 079.A-0192 and 081.A-0734.