Until 1965, steam engines and loose-coupled trucks (generally looking extremely dishevelled / neglected). After the UTA abolished all internal goods traffic and the Derry Road closed, MPD cars (2 or 3 together) were used generally, but as the 1970s progressed, these were gradually replaced by 70 class cars. Waterside station in Derry usually had a single MPD car as a shunter in the late sixties and early seventies.
The CIE engine would bring the Derry goods as far as Lisburn, where it would be left in the back platform for the UTA / NIR railcars to pick up. CIE locos worked the Belfast goods first to Grosvenor Road, later to Adelaide. The CIE engine shunted Belfast after 1972; the ex BCDR diesel plus the CIE loco before that, and steam up to about 1968/9, usually Jeeps.
The CIE motive power was usually pairs of 121/141/181s.
As mentioned, very short lived timber traffic operated in the 1990s. I am not sure of the exact dates. This traffic, plus fertiliser traffic was also operated between Dundalk and Lisburn by CIE / IE, but as the 70 class cars were withdrawn in the early 1980s, NIR diesels took over. The three Hunslets had a turn, especially 102 but rarely 103; later the three 071s (111/2 especially; 113 less often). The second hand C class locos were occasionally used in the mid 1990s.
By the time the Adelaide goods traffic ended (was that, I think, about ten years ago?), motive power was still inevitably “pairs” - variously 121, 141 and 181 classes. I recall 133 & 135 on it quite often, but I’m sure they all had a go.
I never once saw a CIE / IE 071 on goods in the north. I can’t say with certainty that not one ever did, but I think it unlikely. If an 071 ever DID deal with goods to the north, it would have been an extremely rare one-off. Perhaps others might be able to clarify this.