Let's look at that couple of years of peaceful protest by Northern Ireland Civil Rights Association.

It was founded on 29 January 1967 at a public meeting in the International Hotel, Belfast.
The meeting was attended by all political parties in Northern Ireland, although the Ulster Unionist Party delegate Nelson Elder withdrew over a dispute about capital punishment

Wiki describes The Northern Ireland Civil Rights Association as 'an organisation which campaigned for civil rights for the Roman Catholic minority in Northern Ireland during the late 1960s and early 1970s' in a conscious imitation of tactics used by the American Civil Rights Movement'

On 20 June 1968 Austin Currie, a Nationalist MP at Stormont, and two local men occupied a house in Caledon, Tyrone, in protest over its allocation by the local council to a nineteen-year-old unmarried Protestant, Emily Beatty, who was the secretary of a local unionist politician while more than 250 people were on the waiting list in the Dungannon rural district.
The Catholic Goodfellow family had just before been evicted from the house next door where they had been squatting

As a follow up to this the first civil rights march in Northern Ireland was held on 24 August 1968 between Coalisland and Dungannon.

Loyalists organised a counter demonstration in an effort to get the march banned and in fact the planned rally was officially banned, a tactic repeated many times subsequently, although on this occasion the march went ahead illegally without incident

Over the end of August and beginning of September the NICRA and the Derry Housing Action Committee organised a march to be held in Derry on 5 October 1968.

On the 1st of October, the Protestant fraternal organization, the Apprentice Boys of Derry, announced their intention to march the same route on the same day and time, in an attempt to get the civil rights march banned.
The Northern Ireland Home Affairs Minister responded and banned the civil rights march from the city centre.

When the civil rights marchers attempted to defy the ban, they were baton-charged by the Royal Ulster Constabulary who injured many marchers, including West Belfast MP Gerry Fitt.
Television pictures of the march taken by an RTÉ cameraman shocked viewers across the world

Radicalized by these events a more radical civil rights organization People's Democracy was formed on 9 October 1968 at Queen's University Belfast

In imitation of Martin Luther King's Selma to Montgomery marches, about 40 PD members held a march between Belfast and Derry starting on 1 January 1969.
It was repeatedly attacked along the route but whilst passing through Burntollet on the 4th of January, 1969 was 'ambushed' it is reported by 200 Loyalists in 'scenes which horrified nationalists and the world.' as unarmed marchers were beaten with crowbars and lead piping apparently aided by the police.

THE ATTACK 'Next time, it will be the last rites'

Following these events the non-violent politics of the NICRA rapidly became submerged

Nevertheless, NICRA campaigned against internment following its introduction on 9 August 1971.
At a NICRA anti-internment march in Derry on 30 January 1972, 13 unarmed demonstrators were shot dead by British troops, in what became known as Bloody Sunday.

The demonstration marked the effective end of NICRA, though also led to the end of Stormont Parliament that had passed the discriminatory legislation in the first place.