  We discuss the possibility of cogenesis 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 MSSM 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
$Z'$ resonance while $\sigma(\mu^+\mu^-\to e^+e^-)$ is devoid of this
resonance. 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.
