No details whatsoever have survived about their coaches and wagon stock, though given the norms of the time the latter are likely to have been grey or black.
As with many early railways, given that the passenger clientele were to some extent illiterate, or only able to read the Irish language (so studiously avoided by railway companies!), it is possible that like the early BCDR, D & KR, W & TR, etc., the carriages were colour-coded according to class. However, no confirmation of this appears to be extant.
As far as the locomotives are concerned, they had two second-hand Ulster Railway locos at one stage, which like most of their own stock proved to be very unsatisfactory, but that's another story - so these two would have been in the Ulster's brick red livery, probably something like the 1950s / early 60s Isle of Man loco red. It is probable that their own locomotives were a green colour of some sort, probably a dark emerald green, as this was then common. I am unaware of any other information regarding this company.