The way to think about this is: what would happen to the family if stay-at-home Mom were to die. You obviously can't do anything about the loss, grief and trauma, but think about the financial implications.
Assuming that Dad continues to work, and that the child is young, you are going to have to find someone to take care of him/her. If you have relatives willing to step in, that may be fine. but if not you will have to pay for daycare - an expense you don't now have. That's going to get less as the child goes to school, but not go away until he/she is old enough to look after themselves.
Bringing up a child, as well as working a full time job, is pretty demanding. You may find that you don't have as much time for cleaning the house, cooking or other chores. Having a sum of money which can be used to hire help or pay for a few meals out can be very useful in these cases.
Here is an article which places a value on the work done by a stay-at-home Mom. You might not need to pay for all of those services, but it gives you an idea of what the extra expenses might be.
Think about what extra money you might need to spend, and arrange for life insurance to cover it.