Based on nucleons ($p$, $n$) and hyperons ($\Lambda$, ${\Omega }^{-}$) formed at kinetic freeze-out from a quark combination model, we systematically study the production of light nuclei and hyper-nuclei in the hadronic coalescence picture. We present the analytical formula of the nucleus momentum distribution of two-body coalescence and that of three-body coalescence. We explain the experimental data of the transverse momentum spectra of deuteron ($d$), triton ($t$), helium-3 (${}^3$He), and hypertriton (${}_{\Lambda }^3$H) measured in Au-Au collisions from the RHIC Beam Energy Scan I and II, and also provide the corresponding predictions of different $\Omega -$hypernuclei $H(p{\Omega }^{-})$, $H(n{\Omega }^{-})$, and $H(pn{\Omega }^{-})$. We further study the production correlations of different species of light (hyper-)nuclei and discuss their interesting behaviors as a function of collision energy.