The single carrier-frequency division multiple access (SC-FDMA) system is a new system that was adopted in the standardization of the upcoming 3GPP long-term evolution (LTE). Designing diversity-achieving schemes for the SC-FDMA system is a challenging task. The codes adopted should not affect the peak-to-average power ratio (PAPR) among other constraints. In this paper, we consider the design of cooperative diversity schemes for SC-FDMA systems in the uplink direction. Specifically, two relay-assisted distributed space-time/frequency codes are proposed. The proposed distributed space-frequency code (SFC) achieves full spatial diversity in the uplink fast-fading channels, where a diversity of order three can be achieved. The proposed code keeps a low PAPR, which is a good feature of the system. A minimum mean square error (MMSE) decoder is used at the receiver of the destination node. Moreover, we propose a bandwidth-efficient distributed space-time code (STC) for slow-fading relay channels. A decode-and-forward (DF) protocol is used at the relay node, and the possibility of erroneous decoding is taken into account. Simulation results demonstrate the performance improvement of the proposed schemes.