ο Abstract-Microgrids (MGs) with distributed energy resources (DERs) offer multiple advantages in terms of energy efficiency, reliability, and sustainability. However, due to the changes DERs bring to the fault currents, ensuring protection for DER-rich distribution grids is more challenging than conventional grids. This paper investigates the implementation of directional overcurrent relays (DOCRs) in MGs, considering the transient stability of the DERs. Given the low inertia of the DERs, the high operating times of DOCRs can potentially impede DERs' stability, even at post-fault. As such, this paper proposes a novel approach using shifted user-defined characteristics of DOCRs that employs two inverse curves to maintain both relay-relay coordination as well as DERs' stability. Then, the critical clearing times of DERs are combined with the coordination constraints to determine DOCR's optimal settings using genetic algorithm. The proposed methodology is evaluated using the modified IEEE 33bus test system equipped with four synchronous-based DERs. DigSILENT and MATLAB are used to simulate the system, solve the optimization problem, and analyze transient stability. The results indicate the superior performance by the proposed characteristics in comparison with single characteristic to meet both relay coordination and DERs' stability requirements.