[en] We study a possible dark matter candidate in the framework of a minimal anomalous U(1)' extension of the MSSM. It turns out that in a suitable decoupling limit the Stueckelino, the fermionic degree of freedom of the Stueckelberg multiplet, is the lightest supersymmetric particle (LSP). We compute the relic density of this particle including coannihilations with the next to lightest supersymmetric particle (NLSP) and with the next to next to lightest supersymmetric particle (NNLSP), which are assumed to be almost degenerate in mass. This assumption is needed in order to satisfy the stringent limits that the Wilkinson Microwave Anisotropy Probe (WMAP) puts on the relic density. We find that the WMAP constraints can be satisfied by different NLSP and NNLSP configurations as a function of the mass gap with the LSP. These results hold in the parameter space region where the model remains perturbative. (orig.)