Several distinct Garside monoids having torus knot groups as groups of fractions are known. For
two coprime integers, we introduce a new Garside monoid
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
and for dihedral Artin groups of even type.