My soon to be 6 year old daughter surprised me the other day. I was at a friend's house, and he plunked her on an old and (out of tune) piano to distract her while we worked on fixing a model airplane.

Unlike 5 year old me who just hit random
keys and made an ungodly racket with a piano, she was playing actual recognizable music. No dynamics, but the notes were there and mostly correct. She has a little recorder training, but that's it. One of the songs she played by ear, and correctly!

Working in a music store and having 8 years of formal
music training in horns and guitar (despite no talent), I know a little, having sold instruments for a year or so. Yesterday I bought her a good old Roland digital piano for $300, need to print a weight for one of the keys and it is good as new.

I grabbed the first book of the Alfred kid's method my old store used, my wife and I know enough to teach her for a couple years unless she really takes off. I last sold a piano in 2005, so I imagine a few things have changed since then. I feel like she probably would not love Suzuki based on what I know about it, but does anyone have book or method suggestions?

FWIW, she is on the spectrum, exceedingly smart, but very intolerant of "busywork" and excessive repetition.

Personally if I were teaching a really smart kid how to play music I would start with reading standard notation, and scales, chords, and modes.  I wasted years of my life under piano teachers with those lesson books meant to teach idiots these building blocks one bite at a time and didn't learn anything about real music until I was playing guitar under a much more accomplished musician and teacher a decade later.

Now I just play punk rock which is more interesting and fun than jazz anyways.

I treat piano like guitar. First I ask what they really want to learn.

If it's just how to play songs, I just teach chords.  

If they want to play Moonlight Sonata or need to be able to play hymns for church, I go through the lesson books so they learn how to read music.

For reference, we have a bunch of old learning books that are probably as old as the piano.  We also bought Suzuki piano book 1, since my kids use Suzuki for violin.  Suzuki has some neat tunes, and so do the others.  If you don't think she'll enjoy the monotony of trudging through a book, just have her pick what she wants to play and bring her up to speed fast. Patience is key, and I'm guessing you already are practiced with patience.

I swear you just describe me as a child, and it has carried through to my adult life.  I was always bored even in grade school.  I was always ahead of everyone my age because i had 2 older sisters and they would always come home and play school with me and teach me everything they learned. It turned into problems when I had to do things over and over and over.  I couldnt take it and just gave up. This happened while trying to learn guitar at a very early age. To this day I wish I had stuck to it but I just couldnt. Today I just call it having the attention span of a goldfish.

I am less onto the spectrum than her, but I was able to figure out why it was important for me to do zillions of repetitive math problems, or play scales/exercises over and over, in my single digit years.

I do have a short but intensely focused attention span myself, it can be immensely useful in my work, eg inspecting boards/boxes/vehicles for defects, or trying to run down a bug or syntax error in computer code.

Working and going to (engineering) school with some other spectrum dwellers has taught me a great deal of appreciation for their talents.

It is very hard raising a child like that, the flexibility one needs as her teacher, along with patience, can be very very tough some days. I certainly won't  exasperate her with a method or book if it doesn't go well. If she wants to learn songs, that's what she'll do. I want her to find the joy of music.

I'm 99% sure that's why I got this kid. I need to learn more flexibility and patience.

It is rewarding though when she truly gets or understands something complicated like music or mathematics and then crushes it. Makes the fit later in the day that would make a bad 2 yr old proud marginally less terrible