During the time before firearms the rights of rioters had little weight. Belisarius during the Nika riots was an example taken to extremes (if the rioters hadn't gathered in an area with few exits the total number of deaths would have been far lower), but not unique. Although intelligent emperors/mayors/kings etc realised, as already have been mentioned, that to harsh measures could lead to increased violence and/or increased resistance.
For riot control in cities I suppose that Roman legionaries would be best. Big shield, good armour, high level of discipline and the ability to manuver and split into smaller units - you don't want 15 feet pikes in slum areas where the "street" turn each 10 feet. Dash rioters with the shield/fist/flat side of the sword as long as they behave.
In the open country cavalry is far better, at least psychological. Scare and divide the rioters and the problem is probably over.
For a later, pre firearms, riot unit the Shanghai Municipal Police during the Shanghai Concession era seemed to have been good at quelling riots without creating full scale war/bigger riots.