Green’s Dictionary of Slang

(Anglo-Irish) an overcoat; also attrib.

1800s		M. Edgeworth Limerick Gloves ii n.p.: [...] A trusty [...] is [...] a big coat [...] [F&H].
1898		Dave Reed ‘Mister Johnson Don’t Get Gay With Me’ 🎵 ’Cause he saw a lot of vicious niggers feel / Round de trusty pocket, where they keep their steel.
1943		(con. 1850–60s) G.A. Little Malachi Horan Remembers 15: He would wear a ‘trusty,’ or as you would call it a cotamore – the name the people had on it hereabout was a ‘bang-up.’ This was a frieze coat that reached the ankles and which had attatched to it a cape to the wrists.