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