  Let $\overline{p}_{j,k}(n)$ denotes the number of $(j,k)$-regular
overpartitions of a positive integer $n$ such that none of the parts is
congruent to $j$ modulo $k$. Naika et. al. (2021) proved infinite families of
congruences modulo powers of 2 for $\overline{p}_{3,6}(n)$,
$\overline{p}_{5,10}(n)$ and $\overline{p}_{9,18}(n)$. In this paper, we obtain
infinite families of congruences modulo power of 2 for $\overline{p}_{4,8}(n)$,
$\overline{p}_{6,12}(n)$ and $\overline{p}_{8,16}(n)$. For example, we prove
that, for all integers $n\geq 0$ and $\alpha\geq 0$, $$
\overline{p}_{4,8}\left( 5^{2\alpha+1}\left( 16(5n+j)+14\right) \right)
q^n\equiv 0\pmod{64}; \qquad j=1,2,3,4.$$
