Generally, carronades were not used in sieges because of their short range. However, as with anything to do with British artillery, there are exceptions. At Fort Erie in 1814, the RA deployed two 32-pdr carronades as siege weapons, an 8-inch howitzer (iron), an iron 8-inc mortar, and two 24-pdr brass guns.
The latter were experimental pieces cast in the mid-18th century and were only six or so feet long. Four were sent to N America in the late 1770s to equip Burgoyne's army but he did not use them so they went into store, only to be hauled out during the War of 1812 and used as field artillery. Two divisions were in service throughout the last two years of the war but nobody really liked them as they were too heavy for field pieces, besides which they needed more horses and thus more forage. They were not good for siege pieces as they were too short and did not have enough muzzle velocity to have impact.
An officer who watched the bombardment of Fort Erie with these weapons compared it to throwing tennis balls at a stone building.