  We give an infinite family of non-abelian strongly real Beauville $p$-groups
for every prime $p$ by considering the quotients of triangle groups, and indeed
we prove that there are non-abelian strongly real Beauville $p$-groups of order
$p^n$ for every $n \geq 3, 5$ or $7$ according as $p \geq 5$ or $p =3$ or $p
=2$. This shows that there are strongly real Beauville $p$-groups exactly for
the same orders for which there exist Beauville $p$-groups.
