The strum pattern for the rhythm part is largely down-up-chunk-up-down-up-chunk-up. If you're wondering what a "chunk" is, here's an explanation:
In the video he's playing a strum pattern that's a little more complicated that what we'll be playing. We'll just be playing a steady beat, with chunks on the 2 and 4 beats.
Here are the two parts in tab notation, and an MP3. My recording and playing skills aren't much, so unlike Dave, I let my computer generate the audio. It doesn't exactly sound like ukuleles, but I think you'll get the idea.
Since it's only two parts, I've included them both on one recording. If you want to hear just one or the other part for practice, just set your audio balance all the way to the left or right.
Rhythm tab
Lead tab
MP3