I know there are websites for teaching students with dyslexia, but are there any focusing on issues special to music, and particularly piano?
Seems like this article (PDF) was practically written for this question. Here are some quotes that stand out to me immediately on scanning the article (bold emphasis mine, italics are sic):
Two main publications are to be recommended to those who are interested in music and dyslexia. One is Instrumental Music for Dyslexics: A teaching handbook by Sheila Oglethorpe which is full of useful suggestions for teaching children with dyslexia and which she has condensed into an excellent article, Helping dyslexic pupils to succeed. The other is Music and Dyslexia: Opening new doors by Tim Miles and John Westcombe which is a fascinating set of case studies. With the addition of four research papers by Leonore Ganschow et al, Birgit Jaarsma et al, Katie Overy, and Gill Backhouse, these comprise virtually all the literature in the field.
...the Suzuki approach does seem to address many of the problems identified in the research literature for young musicians with dyslexia...
not using any music notation at the beginning level may be a very effective method for developing important listening skills.
That article and referenced books are not web sites themselves, but they do seem to address the issues of dyslexia and learning music.
Suzuki is great for people who have trouble processing the written notes. It is much easier to learn to read written notes when music as a spoken language already makes sense to you. But to teach with the Suzuki method, you need specialized training. And your student wants to start now.
You may need to try some easy beginning piano method books, and incorporate some of the basics of the Suzuki approach:
Have the student listen to the assigned material every day. If the books you choose don't come with a CD, you can record the fragments and pieces yourself.
Choose pieces that have words, and write down the lyrics in the student's notebook, along with some fingerings, and perhaps some simplified notation indicating stress (for example at the beginning of each measure). Have the student sing the pieces -- this will help with learning by ear.
Suggest to the student (if mature) or the parent (if the student is young) that a teenaged musician be hired to be a practice partner several times a week.
Or record a practice tape recording for your student, in which you walk him or her through each activity. In some activities you would have the student play with you, and in some you would have the student listen to a recorded phrase and then respond. In this latter case, you would imagine the student responding, so you can leave the right amount of blank space on the tape recording.
The above outline is very similar to the Suzuki method, but it doesn't use the specific progression of pieces of the Suzuki method. What I'm suggesting is that, at least in the beginning, you slow things down a bit.
I would strongly encourage you to get Suzuki trained as soon as possible. Hopefully you'd have completed the first part of the training around the time your student is ready to move out of the intro phase I outlined.
Should a student evince symptoms of inability to perceive or recognize intervals, sequences, or other basic features of written notation, you may wish to look at traditional methods of transmitting repertoire. Many traditional musics (eg: Celtic) do not include a notation system, so the subsequent application of our Western method tends to leave absent areas.
You can research these lacunae at sites like musicnotation.org or on academic websites, there are a number of journal and popular magazine articles as well. Use phrases like 'traditional' or 'community' in your search, and possibly 'oral/aural' teaching.
As a teacher(not piano), I spent a lot of time teaching dyslexics student including some with most extreme cases like dyspraxia. I spent a lot of time learning about the condition from a theoretical aspect which was helpful. I suggest you do that. The other thing is that people suffering from this condition have found little ways to deal with it and asking your pupil about what they do and how the condition affects them is most important. Generally, affected people tend to have problems with what I describe as "space awareness": can't tell right from left, difficulties reading, driving, or anything that involves hand-eye coordination(relevant to your piano learning). However, with practise, they can do very well with any of these activities. The condition has more problems but these are the relevant ones. What you need to do is discuss with your pupil how to translate the Music into their language. If you say crescendo, it'll mean nothing to them as their brain understands but cannot action it. I suggest you make them listen to a crescendo in a most simplest way like maybe clapping or tapping. Using colours is also very useful. Like maybe a colour for the right hand and another for the left. Reading music will be tricky but as a musician reading music, I don't read notes anymore, I read patterns and My brain fills the blanks. In fact dyslexic people read patterns more than words. These days of technology could allow you to use online music, on a tablet where it could be magnified for them to see intervals. I suspect that you could simplify the sheet music which can sometimes be overwhelming, especially for them. Hope that helps. Good luck