  Several distinct Garside monoids having torus knot groups as groups of
fractions are known. For $n,m\geq 2$ two coprime integers, we introduce a new
Garside monoid $\mathcal{M}(n,m)$ having as Garside group the $(n,m)$-torus
knot group, thereby generalizing to all torus knot groups a construction that
we previously gave for the $(n,n+1)$-torus knot group. As a byproduct, we
obtain new Garside structures for the braid groups of a few exceptional complex
reflection groups of rank two. Analogous Garside structures are also
constructed for a few additional braid groups of exceptional complex reflection
groups of rank two which are not isomorphic to torus knot groups, namely for
$G_{13}$ and for dihedral Artin groups of even type.
