The price is normal for private lessson. Many people only need half hour per week. But you want a little cheap. Sent kid to a piano class. Usually it has 6 kids for one class. It is about 20 dollar for one hour class each week. For a younger kid like 4-6, this kind of class is better. less pressure and more fun. Go to private lesson after your kid graduate from there if he still likes it. Music for Young Children - Childrens music schools.
You can pick one registered piano teacher near your home from this web site. http://www.ormtaottawa.ca/Members.htm From my knowledge, the range is from $40~50/hour in Ottawa. If the child is in the level less than 5, then only half an hour is enough (around $20~25/per class), if the level is from 6-9 level, then 45 minutes is needed (around $30~38/per class), so weekly fee is different based on the child’s piano level. Good luck.
I 100% agreed with Timothy. MYC (Music for Young Children) is a good introduction and inexpensive piano lessons for small children. However, it is important to have a good teacher; this will make the lessons fun and the children willing to learn. You should interview a few MYC teachers before you decide who to go with.