In this paper, we introduce a derivative-free RMIL conjugate gradient method designed for nonlinear systems of monotone equations with convex constraints. The proposed method represents a refinement of the RMIL method through its integration with projection techniques and a derivative-free line search strategy. When certain reasonable assumptions are satisfied, we can prove the global convergence of the proposed method. Numerical experiments demonstrate that the method is highly effective. Moreover, we employ the method to solve sparse signal restoration problems.