In response to the security blind zone challenges faced by traditional reconfigurable intelligent surface (RIS)-aided covert communication (CC) systems, the joint distance-angle beamforming capability of frequency diverse RIS (FD-RIS) shows significant potential for addressing these limitations. Therefore, this paper initially incorporates the FD-RIS into the CC systems and proposes the corresponding CC transmission scheme. Specifically, we first develop the signal processing model of the FD-RIS, which considers effective control of harmonic signals by leveraging the time-delay techniques. The joint distance-angle beamforming capability is then validated through its normalized beampattern. Based on this model, we then construct an FD-RIS-assisted CC system under a multi-warden scenario and derive an approximate closed-form expression for the covert constraints by considering the worst-case eavesdropping conditions and utilizing the logarithmic moment-generating function. An optimization problem is formulated which aims at maximizing the covert user's achievable rate under covert constrains by jointly designing the time delays and modulation frequencies. To tackle this non-convex problem, an iterative algorithm with assured convergence is proposed to effectively solve the time-delay and modulation frequency variables. To evaluate the performance of the proposed scheme, we consider three communication scenarios with varying spatial correlations between the covert user and wardens. Simulation results demonstrate that FD-RIS can significantly improve covert performance, particularly in angular-overlap scenarios where traditional RIS experiences severe degradation. These findings further highlight the effectiveness of FD-RIS in enhancing CC robustness under challenging spatial environments.