Motivated by the recent concept of Space-Time Shift Keying (STSK), we propose a novel cooperative STSK scheme, which is capable of achieving a flexible rate-diversity tradeoff, in the context of cooperative space-time transmissions. More specifically, in our cooperative STSK scheme each Relay Node (RN) activates Decode-and-Forward (DF) transmissions, depending on the success or failure of Cyclic Redundancy Checking (CRC). We propose a novel bit-to STSK mapping rule, where according to the input bits, one of the Q pre-assigned dispersion vectors is activated to implicitly convey log2 Q bits, which are transmitted in combination with the classic log2 L-bit modulated symbol. Additionally, we introduce a beneficial dispersion vector design, which enables us to dispense with symbol-level Inter-Relay Synchronization (IRS). Furthermore, the Destination Node (DN) is capable of jointly detecting the signals received from the source-destination and relay-destination links, using a low-complexity...