This paper considers downlink of reconfigurable intelligent surface (RIS) assisted cooperative non-orthogonal multiple access (CNOMA) systems. Our objective is to minimize the total transmit power by jointly optimizing the active beamforming vectors, transmit-relaying power, and RIS phase shifts. The formulated problem is a mixed-integer nonlinear programming (MINLP) problem. To tackle this problem, the alternating optimization approach is utilized to decouple the variables. In each alternative procedure, the optimal solutions for the active beamforming vectors, transmit-relaying power and phase shifts are obtained. However, the proposed algorithm has high complexity since the optimal phase shifts are solved by integer linear programming (ILP) whose computational complexity is exponential in the number of variables. To strike a good computational complexity-optimality trade-off, a low-complexity suboptimal algorithm is proposed by invoking the iterative penalty function based semidefinite programming (SDP) and the successive refinement approaches. Numerical results illustrate that: i) the proposed RIS-CNOMA system, aided by our proposed algorithms, outperforms the conventional CNOMA system. ii) the proposed low-complexity suboptimal algorithm can achieve the near-optimal performance. iii) whether the RIS-CNOMA system outperforms the RIS assisted non-orthogonal multiple access (RIS-NOMA) system depends not only on the users' locations but also on the RIS' location.