I play a fair amount of Irish guitar backing in DADGAD. I'm not near my guitar at the moment so I'm just thinking it through in my head and I think my main rhythm would be dowm-down-up-down-up as in the Willian Coulter tutor you mention (which I have not seen). However, while generally maintaining this rhythm, I am prone to throwing in little runs, partial chords and variations to try and add a little interest to the basic backing. I also do a variation on this by damping the strings with the heel of my right hand while doing partial chords and runs in the same rhythm on the bass strings. Actually a little easier to do than to describe!
Hope this might help a little.