  This paper shows how to construct coherent presentations (presentations by
generators, relations and relations among relations) of monoids admitting a
right-noetherian Garside family. Thereby, it resolves the question of finding a
unifying generalisation of the following two distinct extensions of
construction of coherent presentations for spherical Artin-Tits monoids: to
general Artin-Tits monoids, and to Garside monoids. The result is applied to
some monoids which are neither Artin-Tits nor Garside.
