It turns out there was already a transcription at The Berrymans' web site. I have tweaked the formatting to suit myself. I also added Lou's introduction from the video.

DOUBLE YODEL
©1995 Lou & Peter Berryman; Words by Peter, Music by Lou

[Lou:] Here's a song we've been doing for quite a while. It's a song that we wrote after we realized that we couldn't yodel. We were really sad until we realized that, cooperatively, we can.

[Peter:] I was once a lonesome cowboy. Ask my cattle.
[Lou:] I was once a cowgirl incomplete and blue,
[Both:] Till the roundup when we came to share a saddle.
Now we do all of the things that sidekicks do.

[Peter:] Plus, not only does romancing go with dancing
[Lou:] On the chaparral without a chaperone,
[Both:] But additionally, it seems to be enhancing
All the thousand things we used to do alone.

[Lou:] Like when I sneeze, I have a guy to say, "Gesundheit!"
[Peter:] Changing a fuse, I found a gal to hold the flashlight.
[Both:] Out of all these, the one that made my pleasure total,
Is that I found I had a pal to help me yodel.

CHORUS: [Peter:] Yodel-a-day [Lou:] ee [Peter:] tee-oh, yodel-ay [Lou:] ee [Peter:] tee-oh [Lou:] oo,
[Both:] We yodel along the trail all day.
[Peter:] Yodel-a-day [Lou:] ee [Peter:] yodel-ay [Lou:] ee [Peter:] oh [Lou:] ee [Peter:] ay [Lou:] ee [Peter:] oh [Lou:] ee [Peter:] ay [Lou:] ee,
[Both:] In an easy double-vocal yodel way.…*

[Lou:] Saturday night when we confuse the palomino
[Peter:] Taking the long romantic way to the casino
[Both:] Riding along we share a jug of Amoretto
[Peter:] And after I sing a line of bass, [Lou:] I sing falsetto. CHORUS

[Lou:] Lucky we are to have each other for assistance,
[Peter:] For when the locals hear us yodel in the distance,
[Both:] And when they say, "That yokel's vocal cords are supple!"
They'd be surprised to find the yokel is a couple. CHORUS

[*There's more yodeling at the end of each chorus which neither I nor the Berrymans (apparently) had the patience to transcribe. -JD

[First appeared on the CD "Double Yodel" in 1995. Re-recorded for "Love Is The Weirdest of All" in 2004. L&PB also sing it on "Laugh Tracks, Vol. 2," a multiple-artists concert album produced by Christine Lavin.]