  We find asymptotic lower bounds for the numbers of both Beauville and
non-Beauville $2$-generator finite $p$-groups of a fixed order, which turn out
to coincide with the best known asymptotic lower bound for the total number of
$2$-generator finite $p$-groups of the same order. This shows that both
Beauville and non-Beauville groups are abundant within the family of finite
$p$-groups.
