The end of the Viking rule in Ireland came with the reign of Árd Rí Brian Ború (Boroimhe). In 980 The Norse suffered a heavy defeat at Tara under the leadership of Brian Ború. Brian Ború became Árd Rí of all Ireland, forcing the petty kings to acknowledge his rule. Eventually even the Norse came under the Árd Rí's rule, for by 1000 Brian was king even of Dublin.

In 989 AD, Sigtryggr Silkiskegg, son of Óláfr Curran became ruler of the Vikings in Dublin. Sigtryggr's rule lasted from 989-993, and from 995-1042. Sigtryggr chafed under the King of Meath, and repeatedly during his reign attempted to throw off the yoke of Meath by allying with the King of Leinster. Meath managed to overcome Siggtryggr's attempts to break free, and Dublin was forced to pay tribute to Meath in 995, 998, and 1000.

It is thought that Sigtryggr was the engineer of the alliance between the King of Leinster the Jarl of Orkney in 1014, which led to the Battle of Clontarf.

In 1012 the Irish King of Leinster decided to rebel against Brian Ború, and hired the aid of Siggtryggr. Siggtryggr, fearing Brian Ború's military might, recruited the aid of Sigur?r Digri. On April 23, 1014, the forces of Brian Ború met those of Siggtryggr. Brian Ború and Sigur?r Digri died in the fight. Siggtryggr survived, and Dublin was untouched by the battle. Thus Siggtryggr ruled in Dublin for many years after, eventually becoming the first king in Ireland to mint his own coins. Siggtryggr eventually became a Christian, and like his father ended his life as a monk in the monastery at Iona. Though the Norse continued to live and rule in Dublin, Limerick, and Waterford, they steadily became more Irish and less connected to Scandinavia.

Despite the best efforts of Siggtryggr, Dublin remained a minor political power. However, Dublin grew steadily in importance as a mercantile center. Dublin was especially well-known for its market in luxury goods, and the profits accruing to the ruler of Dublin from its markets made the town an attractive prize for many rulers. Despite losing its importance as a political power, Dublin continued to maintain its mercenary fleet, hiring the fleet to the Irish, Scots, Welsh, and even Normans, all the way up until the dissolution of the fleet at the time of the Norman Conquest.

By 1035, the Viking camp at Waterford had come under Irish control.

http://www.vikinganswerlady.com/Ireland.htm
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References: [AR7],[PlantagenetA]