Aims. Motivated by observations of the drifting pulsating structures (DPSs) in solar radio spectra, we study the electromagnetic (radio) emission generated during tearing and coalescence processes in a flare current sheet. Methods. For numerical simulations, we used a 2.5-D particle-in-cell electromagnetic relativistic code. Numerical data were analyzed by the wavelet methods. Results. It is found that the electromagnetic emission is generated during a coalescence of plasmoids, and it has a quasi-periodic character. Detailed analysis reveals that the electromagnetic emission is produced around the interacting plasmoids just before their coalescence into a larger one. The period in variations of electromagnetic emission corresponds to that of magnetic field at the same region. Reflections of the electromagnetic waves between interacting plasmoids are recognized. The computed and observed periodicities are discussed. The similarity of the DPSs with some radio bursts observed during star flares indicates a broader applicability for this model.