When the 1969-1998 conflict erupted in Northern Ireland the IRA's most immediate supply of weapons came from it's old stocks from the preceding border campaign of the fifties, which was mostly WW2 era allied weaponry, M1 Garands, M1 Carbines, different model Lee-Enfields, Webley Revolvers and the most iconic, Thompson submachine guns. The problem was however immediately two-fold, there wasn't enough guns to cover all the ground effectively and that the IRA split caused two rapidly swelling organisations (and many small independent groups) to compete over a rapidly declining stock of arms and ammunition. There was two "positives" as well however, the scenes of violence caused many individuals who had moved away from the IRA to "donate" arms they had held onto which caused an influx of WW2, WW1 and even pre-WW1 arms, the second positive was that the Royal Ulster Constabulary (RUC, Local police) and Ulster Defence Regiment (UDR, Locally raised army regiment to replace local militia) were armed with WW2 surplus equipment until stocks of SLRs (British variant of the FAL, which used inches instead millimetres) could be made available, giving the IRA and others some parity.
The arms however began to rapidly show their age, The IRA's Thompson's were by this point over forty years old and had spent a good while of that buried in a Belfast garden, on top of age the varied stock had caused an unexpected logistical issue, the majoirty of their weapons used different calibres of ammo, .45 ACP .303, .30-06 and many more, there was simply no practical way to refill stocks once they ran out. An obvious question was then raised, "Where can we buy a lot of firearms, of the same calibre and plenty of ammunition for them?" and an obvious reply was given "The USA".
The US connection wasn't new, the IRA purchased weapons there for almost it's entire existence but smuggling was slow and costly, the prefered method was large scale theft. IRA units would storm arsenals, primarily in the Republic of Ireland but also in the North and even England. For example during an arms raid on the Phoenix park magazine fort on the 23rd of December 1939 netted the IRA over 1,000,000 rounds of ammunition and dozens of firearms, the vast majority of which was recovered. Or in 1955 when the arms dump at the training base in Arborfield, England was hit to the tube of over 80,000 rounds (over 50,000 of which were .303) and over 70 firearms including 10 BRENs, most of which was again recovered. The point to be made here is that while raids could produce huge gains, they were impossible to hold onto especially as time went on and security got better and better.
The IRA (By this point meaning the Provisional wing) began to centre it's arms around the M1 Garand, M1 Carbine and M3 Grease Gun which began to be imported in large amounts(relatively) in 1971. The M3 replaced the Thompsons, while the various rifles were replaced by the light and short M1 Carbine for street clashes, sniper attacks utilized the Garand(Lee-Enfields also filled this purpose but were increasingly side-lined.) The first modern rifle the IRA would deploy in noticeable numbers was the FAL and L1A1 SLR captured from Irish and British security forces respectively (some Irish FALs also "went missing" during this period only to end up in IRA stocks) but the real equalizer was yet to arrive.
1972 was the defining year of the conflict in many ways, the bloodiest by far and first to see an attempt at a ceasefire and negotiation, the year had began with Bloody Sunday when British soldiers opened fire and killed 14 demonstrators in Derry on the 30th of January and by the end would see the IRA's first car bomb, an eleven year old Catholic boy would become the first death from a plastic bullet, large scale several day long gun battles across Belfast, Bloody Friday when IRA detonated 22 bombs in Belfast in just over an hour killing 9 people, the retaliation in the form of Operation Motorman when the army stormed the "no-go" areas across Northern Ireland using over 27,000 soldiers backed with armoured vehicles and engineering tanks but most import for here was the arrival via George Harrison the first stocks of the Armalite AR-18(0).
The peak of security forces casualities and the zenith of the IRA insurgency phase propelled the AR-18(0) to legendary status, gaining the nickname "Widowmaker", the fame of the Armalite dwarfed even the news of the IRA gaining the SKS 2 years later, even the arrival of the M60 later in decade did little to topple the Armalite from it's prime position, not even the arrival of huge stocks AK pattern rifles failed to unseat the Armalite. The only instance of a switch in primacy came when large amounts of the AR-15 began to appear, referred to the same as it's predecessor as "Armalite". The Armalite was seen in hands of IRA members in countless iconic photos and in 1975 even got it's own song, but why did it remain prime even though it was not as world wide iconic as the AK? simple, the bullet lost it's primacy to the bomb.
As time went on the IRA carried out less and less shooting attacks on security forces and relied heavily on explosives or home made artillery, by the time large stocks of AKs were gained the IRA simply didn't need them, it was over armed. When the time came to take a propaganda photo or video then it was preferable to take out the much more locally famous Armalite than the worldwide AK. While the AK did mostly replace the Armalite as the US supply line became increasingly strained and the middle eastern supply line stepped up to take the slack it was simply too late to unseat the Armalite in popular culture.
In short summary, the Armalite became prime because of the existing US arms supply line and stayed prime because of the dominance of the bomb for the rest of the conflict.