There is evidence of two sugar refining premises in Belfast, both established in the second half of the 1600s, both still working in 1808, but both out of business by 1811.
One was on the corner of Rosemary Lane (now Street) and North Street, the other on the corner of Waring Street (previously Broad Street) and Sugarhouse Entry (which ran between Waring St and High St, close to the Northern Whig). [Adjacent image İBob Ross]

Black George McCartney ran the Waring Street sugarhouse up to his death in 1683. In 1678 he had leased adjacent land called Wilkins tenement in order to extend the sugarhouse. His sons Arthur & Chichester McCartney inherited the premises.
Although it was rebuilt in 1704 (as the New Sugar House), I have no evidence yet of who ran the sugarhouse through to 1792, when again it appears to have recently been rebuilt.
In the last quarter of the eighteenth century six McClean brothers from the Randalstown district arrived in Belfast and became successful merchants and speculated on land leases. Two of these were Samuel and Andrew McClean, wine and spirit dealers at No.1 Sugarhouse Entry, who signed this lease ...

In 1805 the directories show that Montgomery and Tennent were still refining there with Maxwell as partner, though only Montgomery & Tennent 1806-8.

Although dating from before 1704, the Old Sugar House, as it seems it was always known as, in Rosemary Lane, was clearly defined in a lease of 1755. The Donegall Estate leased to Benjamin Legg a plot of ground extending along the west side of North St for 108 feet and bounded on the south side by Rosemary Lane. Specifically mentioned are house, sugarhouses, warehouses and other houses. Legg's Lane ran next to the sugarhouse from Rosemary Lane. Legg died in 1760 and his obituary stated that it was chiefly owing to his skill and activity that the refining of sugar was brought to such perfection in Belfast.
After his death a succession of companies ran the sugarhouse through to 1808 ... Stewarts, Thomson & Co to 1793, Francis Jordan & Co to 1799, and then James Kilbee & Co. Francis Jordan & Co put £5600 into the business, Jordan himself being the refiner and taking £50 a year in wages plus a new free house next door and 5% on profit, coals and candles. James Kilbee & Co, on obtaining the business, put in £9800. Kilbee was the refiner and had previously gained his experience of refining from his time as book-keeper to Stewarts, Thomson & Co.

Those prosperous times were brought to a halt in the first decade of the 1800s, for although the Belfast industry was keeping that part of Ireland (there were also refineries in Dublin and Cork) self-sufficient in refined sugar, the much acclaimed Acts granting free trade with the American Colonies were soon countered and completely defeated by an arrangement of duties and bounties favouring mainland Britain's refining industry.
It seems both sugarhouses closed soon after 1808, for Belfast histories make no mention of them after this date (Dubordieu 1811, Benn 1823). Interestingly, Deerr, in his History of Sugar, makes no mention at all of these Belfast concerns, which each appears to have run for well over 100 years.

Sources ...
Belfast Telegraph, 14 September 1926.
Belfast Directories online.
'History of Sugar', by Noel Deerr, 1949.

[My thanks to Steve Aldridge for his assistance and interest in this research.]
[Postcard image of Sugarhouse Entry, Belfast, İBob Ross]
[My thanks to John McClean of Sydney, Australia, for the McClean family history.]

"The Old Sugar House Company offered £52 10s reward to anybody giving information as to who started the rumour that a man fell into a pan of sugar and was boiled to death and that the sugar was afterwards sold." (Laws & Documents of Old Belfast)