After a bloody civil war and partition in the 1920s, Northern Ireland had about 40 years of peace. This was despite the many grievances that the Catholics had at that time. This resulted in violence in the 1970s. Why did it take so long for the violence to happen?
Revolutions and uprisings tend to occur when youth population booms coincide with political or economic oppression. Ireland had a post-WWII baby boom like many Western countries and the 1970's was when enough of those people were in their twenties and unhappy with the situation they were born into.
There is something unique about being between 15 and 30: the energy of youth, not having the responsibility of children yet, the desire for mobility whether the system you live under allows it or not. You can read a brief summary of the "youth bulge" concept in this article from the Council on Foreign Relations.
You could also read:
There are numerous articles out there that apply this concept to everything from the 2011 Arab Spring, to the uprisings of 1968, to what many expect will be coming up soon in Pakistan, Saudi Arabia, the Pacific Islands, and Africa.
I think a few issues were important in the timing of the Troubles. Free secondary education came in after World War II and this helped create a vibrant, Catholic middle class. The civil rights movement in America was hugely influential and this came together with a housing crisis which highlighted the discrimination in the allocation of council housing. In 1966 the UVF initiated a bombing campaign which it blamed on the then dormant IRA. Into this heady mix entered the Rev. Ian Paisley and the rest, as they say, is history.
I'm gonna guess the Depression of the 1930's, WWII and the aftermath that lasted well into the 1950's. From there, actual growth in Wester Europe and the US probably kept folks decently employed.
The social and economic turmoil of the late 1960's and early 1970's was a common theme across western society.