Cork's compact terminal has spoiled me for years, but there's no getting around the fact that reaching it in comfort from Austin requires a thoughtful connection strategy. There's no nonstop option here, and anyone booking business class from Austin to Cork needs to understand that upfront: this is a one-stop journey routed through a major East Coast or European gateway, with total travel time (including the layover) typically running well beyond the 8.5-hour flying segment. American, Delta, and United all serve this corridor effectively, each funneling Austin passengers through their respective hubs—American via Charlotte, Philadelphia, or New York JFK; Delta via Atlanta or JFK; United via Newark or Chicago—before a transatlantic hop and a short regional connection into Cork, since none of the big three fly the widebody transatlantic leg directly into ORK. Aircraft on the long-haul segment vary by carrier and season, but expect Delta's A330 or A350 business class, American's 777 or 787 Business/Flagship-style cabins, or United's Polaris seating on their 767 or 777 fleet, depending on which hub and month you're flying.
My strongest recommendation, after flying this route repeatedly, is to route through Dublin rather than Shannon connections when possible, then take the short Aer Lingus Regional or a rental car down to Cork—Dublin's transatlantic infrastructure and immigration preclearance (for US-bound return trips) make it dramatically less stressful than scrambling through a smaller connection point. An insider tip few mention: flying into Dublin allows you to clear US customs and immigration before departure on the return leg, meaning you land back in Texas as a domestic passenger, which saves real time and hassle at Austin-Bergstrom on arrival.
January through March and October into November consistently offer the softest business class fares on this corridor, as leisure demand to Ireland dips outside summer festival season and Christmas. Given the multiple carrier options and hub variability, fares shift often—setting up fare alerts for this specific Austin-Cork corridor will serve you far better than manually checking every few weeks.