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In continuation to our earlier reported data on the electric dipole (E1)matrix elements and lifetimes of the metastable states of the alkaline earthions in [Atomic Data and Nuc. Data Tables {\bf 137} (2021) 101381], we presenthere the tune-out and magic wavelengths of the Mg$^+$, Ca$^+$, Sr$^+$ andBa$^+$ alkaline earth-metal ions by determining dynamic E1 polarizabilities.Furthermore, we have evaluated the electric quadrupole (E2) matrix elements ofa large number of forbidden transitions using an all-order relativisticmany-body method and compare them with the previously reported values for a fewselective transitions. Compilation of both the E1 and E2 transition matrixelements, will now provide a more complete knowledge about the transitionproperties of the considered singly charged alkaline earth-metal ions.Similarly, the listed precise values of tune-out and magic wavelengths due tothe dominant E1 polarizabilities can be helpful to conduct experiments usingthe above ions with reduced systematics. Therefore, all these data will beimmensely useful for various applications for carrying out the high-precisionexperiments and laboratory simulations in atomic physics, and interpretingtransition lines in the astrophysical observations.

Tune-out and magic wavelengths, and electric quadrupole transition properties of the singly charged alkaline-earth metal ions