The radiative recombination of donor-acceptor pairs in a weakly doped δn- i- δp- i semiconductor superlattice is detected in time resolved photoluminescence experiments. At short times t ≤ 1 μs, a narrow luminescence line of FWHM = 2.6 meV is measured, which can be related to the width of the filled donor impurity band, formed by mutual orbital overlap. For longer times, a Coulomb induced broadening of the spectra up to FWHM = 6.5 meV is observed, accompanied by a strongly non-exponential decay of the integrated luminescence intensity. The time-dependence of both the spectral width and intensity is in good agreement with a detailed Monte-Carlo simulation of the dynamical processes.