My flute is back from Casey’s workshop…with keys!
I need some tunes with Fnat and/or Eb in them!
This is a serious emergency and I appreciate your support during this time of crisis. 
Doc
http://www.tommcelvogue.com/music/Compositions/reel_06.jpg
I’m sure you’ll find a bunch on this website in general.
The Yellow Tinker! As played on Solas: Solas..
and
The Moving Cloud.. you can play it just fine with D’s in the first part, but the transcriptions usually go from D to D#.
I think Paddy Fahy’s comes to mind…
“Kiss the Maid Behind the Barrel” – a reel in O’Neil’s (the big yellow book). Fantastic tune, 4 parts. 
Cara
It’s good to see that you’re still around Cara, sending you a big smooch 
Tunes using F naturals - Paddy Fahy’s your man, also Paddy Kelly, and quite a few compositions by Ed Reavy. One of the few tunes I’d attempt using both F and Eb keys is the hornpipe “When The Tide Comes In”, also known as “The Factory Smoke” or, recorded by Martin Hayes as “The Brown Coffin”. Good luck.
My favorite tune with an Eflat/Dsharp is Squire Parsons by O’Carolan. It’s available various places on the web – if you want an ABC or PDF without searching, email me.
The Drunken Sailor (per the setting in the The Fire Aflame CD)
I like The Commodore. It’s a reel in D, but the second part has Fnat and Cnat. Don’t know what mode that puts it in. Cherish the Ladies recorded it, among others.
Ming
Here are some of my favorites:
Bare Island (or Bear Island, I’ve seen it written both ways)
Julia Delaney (which gets played almost every session)
Crabs in the Skillet
Fahy’s Reel
The Sunset
If you really want a challenge, try Eileen Curran, a nice reel in G minor, or the Mountain Top, a B-flat major hornpipe.
Sounds like you got a great flute there, Doc! Congratulations!
–James
Les Poule Huppees (a waltz, one of the first tunes I played with keys)
Roslyn Castle
Sandy Brechin’s, Roddy’s Last Trip
John Stevens of Chance Inn (a strathspey, one of my all-time favourites)
Niel Gow’s Lament for His Second Wife
One other suggestion. Try to get hold of the recording by Paddy Carty of Galway. Lots of gems on that, including “Dowd’s Favorite” and the afore-mentioned “Eileen Curran”.
I also love Paddy Carty’s rendition of “Galway Bay” on the other recording with Conor Tully. One of my favourite tunes of all times. It’s in Gminor and it’ll keep you busy for a while.
http://www.thesession.org/tunes/display.php/3453
Claus
The waltz “Pernod” has an Eb in it. Not particularly Irish, I don’t think, but a lovely tune and fun to play.
If you have Cathal McConnell’s CD “Long Expectant Comes At Last,” the liner notes say that he wrote one of the jigs specifically because he wanted to use his Eb key. Can’t remember exactly which tune at the moment, and I don’t have the CD here at work. Then again, without the CD the name won’t do you much good, because you probably won’t find the dots for it anywhere…
Steven
J.S. Bach Flute Sonatas
Sonata in E-Flat Major, BWV 1031
Sonata in Bminor, BWV 1030
Sonata in G minor, BWV 1020
Sonata in A MAjor, BWV 1032
Great craic!
Also Beare Island Reel or Ríl Bhéara. That has Eb and G#. Never played it with an Fnat, so if there’s a setting with Fnat, I’m unfamiliar with it. One of my all-time favorites in any case! 
i’m curious: is Eileen Curran mostly played in G dorian or A dorian? it’s such a fun tune in Ador on a keyless flute; one of those tunes that feels like it was “composed” on a flute.
keylessly yours,
/dan
The first recording of the Eileen Curran (and under the same name) was by piper Tom Ennis on a 78 rpm from the 1920s. He ended it on A.
Fiddleplayers like to play tunes in the ‘darker’ keys sometimes, in this case transposing the tune a tone down, as the yofteen do (around here anyhow) with the Star of Munster. The Star of Munster sounds extremely nice a tone down on the fiddle but in that case I don’t think many would agrue it ‘should’ be played in that key.