We aim to achieve keyless covert communication with a positive-rate in Rayleigh block-fading channels. Specifically, the transmitter and the legitimate receiver are assumed to have either causal or non-causal knowledge of the \ac{CSI} for both the legitimate and the warden channels, while the warden only knows the statistical distribution of the \ac{CSI}. Two problem formulations are considered in this work: (a) Power allocation: maximizing the sum covert rate subject to a maximum power constraint, and (b) Rate allocation: minimizing the power consumption subject to a minimum covert rate constraint. Both problems are formulated based on recent information theoretical results on covert communication over state-dependent channels. When the \ac{CSI} of each fading block is known non-causally, we propose a novel three-step method to solve both the power and rate allocation problems. In the case where the \ac{CSI} is known causally, the power allocation problem can be formulated as \ac{MDP} and be solved using a \ac{DDQN} approach. Although the rate allocation problem under causal \ac{CSI} does not directly conform to an \ac{MDP} structure, it can be approximately solved using the \ac{DDQN} trained for power allocation. Simulation results demonstrate the effectiveness of the proposed power and rate allocation methods and provide comprehensive performance comparisons across different allocation schemes.