This paper presents a new rateless coded cooperation (CC) scheme for the two-user cooperative multiple access channel (CMAC), where two users cooperatively communicate with a common destination. We consider two rateless CC strategies, a fully coded cooperation (FCC) scheme used in the conventional rateless cooperative schemes and a new partially coded cooperation (PCC) scheme. In FCC, each user starts coded cooperation process only after the whole block of the other user's information symbols are fully recovered. In contrast, in PCC, each user starts cooperation as soon as it receives a fraction of new message sent from the other user. The degree distribution for the PCC scheme is designed to maximize the overall system throughput. Simulation results show that the proposed PCC scheme achieves a considerably higher throughput than the conventional scheme in various scenarios.