Hi Louise,
I do have a fair bit of experience teaching this age group, and yes, it can be done!
(thanks for your confidence in me steve!)

The main trick is not to expect too much each week and be prepared to move
extremely slowly. You will need a tutor book with nice big print, lots of pictures, and an awful lot of repertoire for each section.... I used to use "me and my piano", but you will need to bring your student away from it towards the end of the book, where it goes hands together.... the pieces get too long and too complicated. I have since switched to Alfred's prep course..... a brilliant set of books with the added advantage that you can get hold of alot of supplementary material if your student is slower than the book.
Ok I've attempted to write a short list of helpful suggestions.
deep breath, here goes........
1...you need to be your student's pulse for a very long time, play alongside them alot, count out loud continually, allow them to play slowly but expect them to play evenly.
2.... Don't ask for more than a four bar tune at a time, they will lose concentration and motivation very quickly when faced with a big piece of music
3.... lean over and point out the notes as they go, it helps with their pulse and also with their reading...... I only stop doing this when they ask me to.
4...... explain to the parent that they cannot learn unsupervised. The parent needs to sit in the lesson, understand what is required, and copy your teaching technique at home
5....... explain to the parent about practising...... tweny five minutes a week (not a day!) is fine at this level
6... split the lesson into very short activities, a child this age can keep concentration for a full half hour but not if doing the same thing for that time
7.... get hold of either alfred's ear and activity training book to match the tutor book, or Jane Smisor Bastien' Listens & Creates, and get yourself alot of crayons. Both these books have colouring actvities, the listens and creates are aural based, and the alfred one is aural and notation and keyboard based.
8..... get hold of either monkey puzzles vol 1 (harewood & waterman) or alfred prep course theory. You might think it daft to begin theory at such a young age but kids this age think they're doing a puzzle book not formal theory training.
9.... be enthusiastic!..... I've never been the type of teacher who does well on dancing around the room and stuff but my kids have a whale of a time because I'm have fun teaching them.
10... Use stickers, stickers and more stickers! Most kids this age are seriously motiveted by the thought of getting a sticker in their book and a whole bunch of stickers on their jumpers to show off with when they get home. Buy cheap and use alot of them
11... watch your student carefully for signs that they're losing interest in their task. AS SOON as they do, finish that task on a good note, amd switch tasks. You can go back to the original one later
12.... use duets in the books to lengthen playing time on pieces in lesson and give added interest to the music.
phew, I think that's it........
I might come back later when I've had more coffee and add some in!
Best of luck, and don't listen to anyone who says it can't be done. I've taught this age group alot over the years, and I've now got alot of extremely good pianists in my student base who started at age 4.

hope this helps