This work studies the problems of feedback allocation and scheduling for a multichannel downlink cellular network under limited and delayed feedback. We consider a realistic scenario where a fixed and small number ¯ F of link states can be reported to the base-station (BS) per time-slot. We study the trade-off between knowing at the BS a small number of accurate link states (i.e. that can be reported within one time-slot) and a larger but outdated number of link states (i.e. number of link states > ¯ F that requires more than one slot to be reported). We propose an efficient algorithm that selects the link states that should be reported to the base-station. A novelty here is that this feedback allocation algorithm is performed at the users side. We show that this algorithm combined with the Max-Weight scheduling achieves at least a fraction η of the stability region achieved under the ideal system (i.e. with full and perfect feedback at no cost). We then provide numerical results that show the best aforementioned trade-off under various system setups.