In this paper we present further results from a deep near-infrared imaging survey to look for emission-line galaxies at high redshift. The data consist of IRCAM images taken in the near-infrared J window (1.0-1.5 μm) using four narrow-band (2 per cent FWHM) filters, and covering a total area of 3.0 arcmin^2. This paper presents the constraints on the star formation rate obtained from the upper limits of Hα emission redshifted into our passbands from galaxies between z~=0.5 and 0.9. We search a total volume of ~=586 Mpc^3 (q_0=0.5, H_0=50 km s^-1 Mpc^-1) for Hα to a flux limit in the range (0.9-10.7)x10^-19 W m^-2. This implies a star formation rate <=10 h^-2_50 M_solar yr^-1. From a comparison of these limits with the expected number of galaxies at these epochs, if galaxies undergo significant merging in their history, then the bulk of the galaxy population could not have been forming stars at a rate significantly greater than that found in local galaxies.