The infantry did not have permanent depots until c1873. Before then they would move around the UK every few years.
I have found that in 1861 the 3rd Light Dragoons/Hussars were in Belfast; plus the Depots for the 26th, 49th, 62nd, 63rd and 76th Regiments of Foot.
In 1871, there was one troop of the 6th Dragoon Guards; the 80th Foot and the Depot of the 37th Foot. The 1st Battalion 16th Foot and the Depot for the 55th Foot were elsewhere in the general area.
In addition there would have been elements of all the ‘corps’ – RA, RE, Commissariat, medical, etc.
Ken