We must first ask if the 19th century American environment contained enough fear or hatred of the Irish community to support the existence of the NINA sentiment? Did the Irish-American community constitute an "Other" that was reviled and discriminated against?
Did more modern Americans recoil in disgust at the premodern Irish immigrants? The evidence suggests that all the criticism of the Irish was connected to one of three factors, their "premodern" behavior, their Catholicism, and their political relationship to the ideals of republicanism. If the Irish had enemies they never tried to restrict the flow of Irish immigration.
Much louder was the complaint that the Irish were responsible for public disorder and poverty, and above all the fears that the Irish were undermining republicanism. These fears indeed stimulated efforts to insert long delays into the citizenship process, as attempted by the Federalists in 1798 and the Know Nothings in the 1850s. Those efforts failed.
As proof of their citizenship the Irish largely supported the Civil War in its critical first year. Furthermore they took the lead in the 1860s in bringing into citizenship thousands of new immigrants even before the technicalities of residence requirements had been met. The Irish claimed to be better republicans than the Yankees because they had fled into exile from aristocratic oppression and because they hated the British so much.
The use of systematic violence to achieve Irish communal goals might be considered a "premodern" trait; it angered many people and three bloody episodes proved it would not work in conflict with American republicanism. In 1863 the Irish rioted against the draft in New York City; Lincoln moved in combat troops who used cannon to regain control of the streets and resume the draft.
In 1871 the Irish Catholics demanded the Protestant Irish not be allowed an Orange parade in New York City, but the Democratic governor sent five armed regiments of state militia to support the 700 city police protecting the one hundred marchers. The Catholics attacked anyway, and were shot down by the hundreds.
In the 1860s and 1870s the Molly Maguires used midnight assassination squads to terrorize the anthracite mining camps in Pennsylvania. The railroad brought in Pinkertons to infiltrate the Mollys, twenty of whom were hung. In every instance Irish Catholics law enforcement officials played a major role in upholding the modern forms of republicanism that emphasized constitutional political processes rather than clandestine courts or mob action. In each instance the Irish leaders of the Catholic Church supported modern republicanism.
After the 1870s the Irish achieved a modern voice through legitimate means, especially through politics and law enforcement. Further enhancing their status as full citizens making a valuable contribution to the community, the Catholics built monumental churches (which were immediately and widely praised), as well as a massive network of schools, colleges, hospitals, orphanages and other charitable institutions.
Regardless of their growing status, something intensely real was stimulating the Irish Catholics and only them. The NINA myth fostered among the Irish a misperception or gross exaggeration that other Americans were prejudiced against them, and were deliberately holding back their economic progress. Hence the "chip on the shoulder" mentality that many observers and historians have noted.
As for the question of anti-Irish prejudice: it existed but it was basically anti-Catholic or anti-anti-republican. There have been no documented instances of job discrimination against Irish men.
Was there any systematic job discrimination against the Catholic Irish in the US: possibly, but direct evidence is very hard to come by. On the other hand Protestant businessmen vigorously raised money for mills, factories and construction projects they knew would mostly employ Irishmen, while the great majority of middle class Protestant households in the major cities employed Irish maids. The earliest unquestioned usage found comes from the English novelist William Makepeace Thackeray, using the phrase in Pendennis, a novel of growing up in London in the 1820s. The context suggests that the NINA slogan was a slightly ridiculous and old-fashioned bit of prejudice Other ethnic groups also had a strong recollection of discrimination but never reported such signs. The Protestant (Orange) Irish do not recall "NINA signs. Were the signs used only against Irish targets?
An electronic search of all the text of the several hundred thousand pages of magazines and books online at Library of Congress, Cornell University Library and the University of Michigan Library, and complete runs of The New York Times and The Nation, turned up about a dozen uses of NINA.
The complete text of New York Times is searchable from 1851 through 1923. Although the optical character recognition is not perfect (some microfilmed pages are blurry), it captures most of the text. A search of seventy years of the daily paper revealed only two classified ads with NINA—one posted by a Brooklyn harness shop that wanted a boy who could write, and a request for a couple to take charge of a cottage upstate.