  EuZn$_2$P$_2$ was reported to be an insulating antiferromagnet with
$T_\mathrm{N}$ of 23.5 K. In this study, single crystals of EuZn$_2$P$_2$
exhibiting metallic behavior and a ferromagnetic order of 72 K ($T_\mathrm{C}$)
are successfully synthesized via a salt flux method. The presence of hole
carriers induced by the Eu vacancies in the lattice is found to be crucial for
the drastic changes in magnetism and electrical transport. The carriers mediate
the interlayer ferromagnetic interaction, and the coupling strength is directly
related to $T_\mathrm{C}$, as evidenced by the linear dependence of
$T_\mathrm{C}$ and the fitted Curie-Weiss temperatures on the Eu-layer
distances for ferromagnetic Eu$M_2X_2$ ($M$ = Zn, Cd; $X$ = P, As). The
ferromagnetic EuZn$_2$P$_2$ shows conspicuous negative magnetoresistance (MR)
near $T_\mathrm{C}$, owing to strong magnetic scattering. The MR behavior is
consistent with the Majumdar-Littlewood model, indicating that the MR can be
enhanced by decreasing the carrier density. Our findings suggest that
Eu$M_2X_2$ has highly tunable magnetism and charge transport, making it a
promising material family for potential applications in spintronics.
