In this paper, we propose a frequency controller for lossless microgrids which achieves a desired active power load sharing while regulating system frequency to some nominal value. The control scheme is based on the slow readjustment of the active power reference of each inverter, i.e., each inverter aims to track a slowly-varying reference that is set sufficiently close to its actual active power injection and moved slowly to reach some desired injection value. This way, the control enforces the trajectory to satisfy the so-called phase-cohesiveness property, i.e., the absolute value of the voltage phase angle difference across electrical lines is smaller than $\frac{\pi}{2}$, which ensures that the system remains stable at all times and the actual active power injections track the slowly-varying reference. We also propose a distributed method to find desired injections, which satisfy the phase-cohesiveness property for tree networks as well as for some cyclic networks. We also discuss implementation aspects of the proposed control scheme and demonstrate its feasibility using a 9-bus microgrid.