Okay, I admit it, I’ve been playing some non-traditional music on my tin whistle, and I don’t know what to do when I get to a note that is lower than “D”. 
So far I’ve just played “D” for all notes that are “D” and lower, but I’m wondering what others do? Or maybe I’m the only one out there playing non-traditional music…it sure helps me practice though… 
If you need to play lower, just sit down. Or even sprawl on the floor. for anything lower than low, you’ll probably need to go down to the basement.
Transpose the note (or the whole phrase) up an octave.
If you’re playing in a key that needs accidentals your whistle doesn’t have you’ll also need to experiment with alternate fingerings.
Transposing up an octave isn’t that big a deal, and you can often do it on the fly if you’re a decent sight-reader - if not, just memorize it (you plan to memorize that song anyway, right?)
If you want to play non-trad tunes in keys with lots of accidentals, you might want to seriously consider picking up a recorder - a plastic soprano recorder plays in much the same range as a D whistle (except for differences in fingering it’s almost like one of the 7-hole whistles that have been discussed in other threads lately, with an added thumb hole for octave control).
Whistles finger faster, allow more elaborate ornamentation, and have (I think) a nicer sound for trad pieces. But once you get outside traditional tunes, a recorder is often a more flexible choice.
I play both, though I have been neglecting the recorder since I got whistle obsessed. But unless you’re really, really, good at half-holing notes like B-flat and G-sharp at speed, a recorder is a better choice when you need them.
Okay, I’m kind of new to this (but already obsessed), so if I understand you correctly, you’re saying to play the C right below D as the C right below high D?
Yep. Depends on what I’m playing whether I flip just the low notes or the whole phrase.
And for some pieces I just play the whole thing an octave higher - if the tune has a two-octave range, it will probably sound better if you move it up than if you flow just the low register (converting it into, essentially, a one-octave tune).
Your whistle has a range of 2+ octaves - might as well use them. Fife pieces, in particular, are meant to be played in the upper octave - see “On the road to Boston” from Bill Och’s Clarke tinwhistle book for a fife piece transcribed for tinwhistle. It’s a good book, especially if you want to move to pieces beyond Irish trad - he’s got fiddle tunes, fife pieces, and English dance tunes mixed in with the Irish and Scottish pieces.
When I have a tune that has notes below low d:
- sometimes I play it an octave higher
- sometimes I split the octave, that is, I play the low notes an octave higher but the rest of the tune as written.
- Sometimes I play part of the tune an octave higher, and part as written. (I do this with “Come by the Hills”.)
- Sometimes I transpose the song into a different key. For example, “Red is the Rose” has some notes that go below D. If I don’t feel like playing an octave higher, I transpose it into key of G.
- If the not is not important, especially if I’m playing with other musicians who have instruments with more range, I’ll substitute a rest for the note I can’t reach. (I do this on King of the Fairies and Scully’s Reel.)
I do whichever is easier and sounds best.
Instead of leaving out the note or taking it up an octave, substituting one of the notes in the guitar chord sometimes works.