We present measurements of the elliptic flow, $v_2$, as a function of transverse momentum ($p_T$), pseudorapidity ($eta$), and centrality in $d$$+$Au collisions at $sqrt{s_{_{NN}}}=$200, 62.4, 39, and 19.6 GeV. The beam-energy scan of $d$$+$Au collisions provides a testing ground for the onset of flow signatures in small collision systems. We measure a nonzero $v_2$ signal at all four collision energies, which, at midrapidity and low $p_T$, is consistent with predictions from viscous hydrodynamic models. Comparisons with calculations from parton transport models (based on the {sc ampt} Monte Carlo generator) show good agreement with the data at midrapidity to forward ($d$-going) rapidities and low $p_T$. At backward (Au-going) rapidities and $p_T>1.5$ GeV/$c$, the data diverges from {sc ampt} calculations of $v_2$ relative to the initial geometry, indicating the possible dominance of nongeometry related correlations, referred to as nonflow. We also present measurements of the charged-particle multiplicity ($dN_{rm ch}/deta$) as a function of $eta$ in central $d$$+$Au collisions at the same energies. We find that in $d$$+$Au collisions at $sqrt{s_{_{NN}}}=$200 GeV the $v_2$ scales with $dN_{rm ch}/deta$ over all $eta$ in the PHENIX acceptance. At $sqrt{s_{_{NN}}}=$62.4, and 39 GeV, $v_2$ scales with $dN_{rm ch}/deta$ at midrapidity and forward rapidity, but falls off at backward rapidity. This departure from the $dN_{rm ch}/deta$ scaling may be a further indication of nonflow effects dominating at backward rapidity.
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