Thanks, all of you, for the good ideas.
To clarify (and add more info):
1) These are the children of one of my bosses at a job where I play piano; and I love the whole family quite apart from any need to brown nose the boss, and I think I could get more students if my boss (their mom) likes my teaching. So far (one month in) she and the kids are very excited about it.
2) I have always felt that a good piano teacher can accommodate students with different needs, and to that end I have always eagerly embraced people with special "requirements" and made it an opportunity for myself to grow as well as for the student to learn to play and love music. I have had some INTERESTING students with INTERESTING needs...the stories I could tell...So this is just another challenge for me, and it is one that I fervently want to meet with everyone involved having fun with the piano-learning process.
3) The 8-year-old is already quite a good reader, and so using printed music is not an issue for him. But the 4-year-old hasn't learned all her letters yet, and is a bit scared of new stuff and new situations where she may fail (a perfectionist already! poor kid...). During the month we have worked, the first few weeks were spent mostly with the older kid, and the 4-year-old was learning what kind of person I am and whether she feels comfortable around me. At the first lesson she was too shy to sit at the bench and do simple things when I asked her to, even with the mom there; so I just bided my time and kept at her by having the mom sit next to her and asking "everybody" (meaning the mom, the older brother, and finally the 4-year-old) to do a particular task like "Find three black keys!!". So at first we weren't sure she would even take to me teaching her; but now, four weeks later, she sits right down and is eager to show me her latest piece. The mom can't believe it. So I can teach her something...But at the beginning I got what I thought was a set of books appropriate for her age, with lots of coloring and tracing and pictures to reinforce concepts I would teach her. Before buying these books I asked the mom: "Can she write her own name?" which is one of the questions I ask to ascertain the reading level of a child. The answer was yes; so I proceeded to buy these books, not realizing that her name was ALL she could write (but she prints it beautifully). I only figured this out when, on a page with the task of finding and coloring "A B C D E F G" she did "A" perfectly well, but with "B" she looked me in the eye and said a little apologetically "I can't do that". It was kind of cute how she did it (made my heart melt a little bit), and I hastened to assure her that that was fine and here is how to print "B"...but Mom stepped in and stopped that process. Apparently the teachers at her school really want to be in complete control of their learning to write. So I thought "OK, I won't have her write anything: I'll just have her recognize stuff, without generating it herself by writing." So I asked about flash cards: would THOSE be OK? The answer was an emphatic no.
4) So I researched for a while about Waldorf's educational philosophy on the Internet, and what I found gave me some options to work with: they like improvisation and "group" music making (recorders and voice are "group", not "isolating" like piano), and they like folk songs a lot. So I can use improvisation to teach some basic technique skills, and can also teach them to play folk songs, and these avenues seem fun and exciting. I'll be creating my own curriculum...but I've done that with every student I've ever had, so it ain't no thing.
I still have personal reservations, as osmisis seems to, about a 4-year-old who doesn't write the whole alphabet; but then there are other child development experts who say that reading too early is damaging (Bev Bos is one). Who knows? What I have to work with is a fun and very smart child who accepts me, as does the rest of her family, as a friend who comes over and teaches piano and sometimes hangs out just for fun with the whole family; so it's worth any "restrictions" because I think I can do something with this kid. Time will tell...