  We have investigated the magnetoelectric properties of
(Ca$_{1-x}$Sr$_{x}$)$_2$CoSi$_2$O$_7$ ($0\leq x\leq 1$) crystals with a
quasi-two-dimensional structure. In Ca$_2$CoSi$_2$O$_7$ ($x=0$), a canted
antiferromagnetic transition occurs at 5.6 K. The transition temperature
$T_{\rm N}$ is increasing with increasing Sr concentration, and the rises of
the magnetization and dielectric constant become larger. Since the dielectric
constant shows large change at $T_{\rm N}$ and the magnetocapacitance effect is
observed below $T_{\rm N}$, a coupling between the magnetism and dielectricity
is strong in (Ca$_{1-x}$Sr$_{x}$)$_2$CoSi$_2$O$_7$. The positive
magnetocapacitance is reduced by Sr substitution, and is not observed in $x\geq
0.5$. Namely, the compound of $x\geq 0.5$ does not show the
magnetic-field-induced electric polarization. On the other hand, the negative
magnetocapacitance is enhanced by Sr substitution.
