Nice post. I'm a piano teacher, but I've also taught the drums and the guitar. I've never taken ukulele lessons, but here's what I'd like to learn/teach:
1. The Swing: The drums were my first instrument, and I could swing by the time I was 14, so at 39, I'm a little removed from the original process. My sister is a mandolin player, and when I taught her the ukulele while we were on a road trip, I spent most of the time trying to get her to swing. Just a basic technique everyone can enjoy. What to do: Start with the basic C/F/Ami/G7 chord progression, and just practice.
2. Sightreading Basic Tunes: With high G tuning, you only have a good octave to play around with. I like the low G tuning because you can play through a good fiddle fakebook. What to do: Start with basic tunes in the key of C, and move on to F, G and other keys.
3. Playing Chords While Singing: I couldn't sing a lick and had no desire to when I bought a $50 Lainikai soprano uke. Now I sing every day, own four ukes and have a nice karaoke setup. What to do: Get over the laughs. DO NOT LAUGH when a student laughs. Smile and encourage him. Photocopy songs out of a fakebook.
4. Play Melodies Higher on the Neck: By learning scale patterns, you can really knock melodies out, especially with low G tuning, where you can play four notes per string and knock out two octaves from G to Eb. What to do: Use the right scale book along with a fiddle tune fakebook. Try to build speed.
5. Beginning Tab Reading: Most people will put this a lot earlier, but I believe in learning to read over all other skills. Since there are so few strings to read basic melodies, you can go a lot with a little. Depending on the skill level and background of your students, you might need to do this before sightreading basic patterns. What to do: Get blank tab paper and have them convert notes to tabs and tabs to notes.
6. Pentatonic Improvisation; You need to get out that scale book and learn a few pentatonic scales. I actually have a scale and chord book for the ukulele, I belive by Hal Leonard, and in a perfect world, it would be about twice as large. What to do: You've got to know improvisation to teach it. Repetition, rhythm and relaxation are key.
7. Beginning Fingerstyle: Start with an open Ami7 chord and play C-E-A-E G-E-A-E, both swung and unswung. This basic fingerstyle pattern will take you a long way as you learn to play chords over the basic pattern. What to do: Break out the fakebook and the vocals again, and practice away.
8. Chord Melodies: Of course, this is where it's at for most ukulele players. There are a lot of good books out there with sheet music, and there are great tabs online. What to do: Find out what your student likes. I'm very fond of From Lute to Uke, but I realize that everyone doesn't have the love of Medieval music I have.
9. Hammer Ons, Hammer Offs, Bends: This is where good sounds come from. I mostly learned these through playing other instruments and brought these skills to the ukulele, but there should be a good book out there explaining this stuff. What to do: Find a good book, or better yet, write one.
10. The Blues Scale I: Riffs: There's a lot of improvisation involved here, too. What to do: Get out the scale book, and study rhythms. Ideally, there should be a lot of reading involved.
11. The Blues Scale II: The Blue Note: I'm a purist. If I can play a pure blue note, which doesn't appear on the piano, I do. It's a 1/4 step away from where most books have it. What to do: Everything from 10., but with the proper blue note.
12. Rolls: I learned about these from playing the banjo, and I reverse-engineered them to the ukulele. It's a weak point of mine. I love the freedom that some of these patterns have with the right hand while holding chords in the left. What to do: I don't know if a book is out there, but if anyone writes one, let me know!
13. Power Chords: I love using these on the guitar, and I sometimes plug my steel-stringed Eleuke into Guitar Rig 5 and plug away. Traditionally, these are played with two or three strings, but it's possible to play them with four, and pretty fun. What to do: This is where your Uke a Day fakebook falls short. You really have to get some guitar music and cut out ukulele tabs to put over the guitar chords.
14. Arranging: Once upon a time, I was a harp player (the stringed variety(, and one of my favorite music books of all time is an arranging book for the harp by Sylvia Woods. I unfortunately stopped playing the harp after a panic attack after playing at my sister's wedding, but I'd love to have the same style of arranging to the ukulele. What to do: I didn't expect to write this long a post, and at this point, I'm practically ready to write a book, or a series of books.
Conclusion: The essence of good teaching is preparation. Teaching the piano is a lot easier for me because the courses are all laid out, but I'm actually interested in teaching the ukulele now.