When solving the Darcy problem in its mixed form, it is well-known that the set of pairs of spaces chosen to approximate the velocity and vector fields is restricted by the necessary and sufficient LBB condition. In order to circumvent this restriction, stabilized finite element methods have been developed. In the tradition of the PGEM methods used to stabilize the [special characters omitted] element for the Darcy problem, the Residual Local Projection (RELP) methods are developed as an approach to stabilization when approximating with equal-order linear spaces using both continuous and discontinuous pressure interpolations. A total of four related methods are presented, two of them being of the two-level type. The methods are analyzed and shown to be optimally convergent. Furthermore, the methods employing a discontinuous pressure present a mass-conservative velocity. Finally, numerical tests are performed to validate the theory and show performance on a real-world problem.