We discuss the possibility of the cosmic coincidence generating the ratio of baryon asymmetry to dark matter in a Stueckelberg $U(1)$ extension of the standard model and of the minimal supersymmetric standard model. For the $U(1)$, we choose $L_{\mu }-L_{\tau }$ which is anomaly free and can be gauged. The dark matter candidate arising from this extension is a singlet of the standard model gauge group but is charged under $L_{\mu }-L_{\tau }$. Solutions to the Boltzmann equations for relics in the presence of asymmetric dark matter are discussed. It is shown that the ratio of the baryon asymmetry to dark matter consistent with the current WMAP data, i.e., the cosmic coincidence, can be successfully explained in this model with the depletion of the symmetric component of dark matter from resonant annihilation via the Stueckelberg gauge boson. For the extended minimal supersymmetric standard model model, it is shown that one has a two-component dark matter picture with asymmetric dark matter being the dominant component and the neutralino being the subdominant component (i.e., with relic density a small fraction of the WMAP cold dark matter value). Remarkably, the subdominant component can be detected in direct detection experiments such as SuperCDMS and XENON-100. Further, it is shown that the class of Stueckelberg models with a gauged $L_{\mu }-L_{\tau }$ will produce a dramatic signature at a muon collider with the $\sigma ({\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-},{\tau }^{+}{\tau }^{-})$ showing a detectable $Z^{\prime }$ resonance while $\sigma ({\mu }^{+}{\mu }^{-}\to e^{+}{e}^{-})$ is devoid of this resonance. Within the above frameworks, we discuss several broad classes of models both above and below the electroweak phase transition temperature. Asymmetric dark matter arising from a $U(1{)}_{B-L}$ Stueckelberg extension is also briefly discussed. Finally, in the models we propose the asymmetric dark matter does not oscillate and there is no danger of it being washed out from oscillations.

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