There are tunes that have this “bluesy feeling” - you could play them after any Blues (eg. “St. James Infirmary” or "House Of The Rising Sun). So far but I only know three: “The Old Bush”, “Rakish Paddy” and “Poll Ha´penny”. Any more? (they all seem to be in A - the key that allows for a Blues-scale)
I find “Rathlin Island” to have a bluesy feel. You can slide into the upper octave E very well. Often paired with Sporting Paddy, like here:
http://www.youtube.com/watch?v=bsdXrNo3-BE (whistle clip)
Then, you always have McGoldrick tunes (maybe not counting):
http://www.youtube.com/watch?v=M4VuLxqYX3w
http://www.youtube.com/watch?v=5asBavWUFKE&feature=related
Thanks, Christian! You made me aware of the fact that its not so much the newer stuff I´m after but moreover the older stuff.
Hah - always happy to help 
Don’t know if I really understand what you’re getting at but the Lonesome Jig is one that comes to mind. Have a listen to Mickey Dunne’s version on YouTube.
In the same sense, try playing a slowed-down version of the jig, the Rolling Wave.
What about “Noel McCarthy’s Jig”, as played by Jerry O’Sullivan on The Gift?
I heard a recording of the Hunters Purse many years ago by Niamh Parsons and the Loose Connections. It started off on low whistle and they put emphasis on particular notes in the tune which gave it a very bluesy feel. It was followed up with Andy Renwick’s Ferret on uilleann pipes which had some bluesy elements as well. This one is worthwhile checking out.