Not sure how much Irish Dempsey had and we know Ali had a least 1/4 but whats your top 10 of guys that were at least half Irish Gene Tunney Mickey Walker Billy Conn etc.
Loughran, Driscoll, McFarland, Kilbane, Mclarnin, McGovern, Burley (irish mother), Tommy and Mike Gibbons, Fitz,...
ALI's mother had an Irish grandfather. So that makes her 1/4th Irish and Muhammad 1/8th Irish. Apparently he is only one generation away from being able to claim an Irish passport. Since all you need is one grandparent to claim dual nationalities So that is pretty Irish. Gene Tunney, Corbett and John L were all full Irish. Jimmy Braddock was 3/4 Irish, I think his parents were English born, his mother to an Irish family and his father English/Irish. Max Baer was 1/4 Irish on his mother's side but mostly German. I don't think Jack Dempsey was very Irish at all. His family were Pioneer stock and a mixture of quite a few generations worth of European and possibly native American cross breeding.
Jem driscoll had Irish parents so can be included. Irish born I'd go for Jimmy mclarnin and steve Collins. Jimmy Braddock was sometimes born in America, sometimes Ireland and at other times Manchester.
Dave Shade. Dave and Spike Sullivan Dominick McCaffrey, Jack McAuliffe, Nonpareil Dempsey, Ike "The Belfast Spider" Weir, Paddy Duffy(first welterweight champ).