Entropy,

I would suggest the Lebanon, where IIRC Syria intervened in the civil war, effectively freezing the situation in Beirut and yes violence lessened, the issues did not go away alas. I am sure Rex B. or Wilf can comment better.

Near to home I would say Northern Ireland, underpinning the UK's response to violence was containment and the prevention of escalation. It took a long time and was a "bumpy" journey. Certainly at the start of the latest round, 'The Troubles' in 1969 few would have foreseen the Good Friday Agreement, let alone today Sinn Fein and the DUP in a governing coalition.

Maybe Cyprus? Further back I think the interventions of the League of Nations in post-1918 Europe merit some attention, Upper Silesia comes to mind and the population transfer between Greece and Turkey.