Cooperative communications is a well known technique to yield transmit diversity in a multi-user environment. Network coding can increase the spectral efficiency in networks. These two techniques can be combined to achieve a double diversity order for a maximum coding rate Rc = 2⁄3 on the Multiple Access Relay Channel (MARC), where two sources share a common relay in their transmission to the destination. However, codes have to be carefully designed to obtain the intrinsic channel diversity. Up till now, no full-diversity capacity achieving code for the MARC at a coding rate Rc = 2⁄3 has been published. We present a strategy to produce excellent low-density parity-check (LDPC) codes with rate 2⁄3, i.e., exhibiting full-diversity and operating close to the outage probability limit. Simulation of the word error rate performance of the new proposed family of LDPC codes for the MARC confirms the full-diversity.