The distinguishing feature of an Irish-style button accordion is that the two rows on the treble side are in keys that are half a step apart. Therefore, on the melody side of the instrument you have all of the notes–in piano terms, all of the white keys and all of the black keys, too. The most common combination is B/C, followed by C#/D. The treble keyboard is generally flat, rather than stepped.
Bass arrangements vary, but typically include bass notes and chords appropriate for the Irish repertoire. Paolo Soprani, McComiskey, Nolan, and Burke are some layouts you might encounter. Check them out if you like: Irish bass arrangments.
Some models have a stop to take out the thirds of the chords in the bass. Because the third defines a chord as major or minor, removing the third essentially allows the chord to be neither. It will lack definition, but it won’t clash.
Castagnari Dinn II B/C walnut
Hohner Double-Ray
Introduction to Concertinas and Accordions 