It is so hard to tell anyone difficult news. There probably is no way to tell her without her being at some level upset -- but there are things that you can do in order to make it more palateable, and better for your friendship in the long run.
I think the two words that will help you are: honesty and consideration. Be honest about the situation, while remaining considerate to her needs for support and help. I would suggest that when you tell her, talk about the difference between what he needs in order to thrive (a quiet focused environment) and what you can provide (active, highly-stimulating environment with two older children). You can say, "I think he needs to be somewhere else," rather than starting from the point that you need him to be somewhere else.
Also, I think you will help both of you if you give her a timeframe: "I will watch him for one month/two more weeks while you find something else for him."
It may be hard. She may be mad at you. But if she really is someone you could be best friends with -- then she should understand that you still want to support her -- but not in this way.
Good luck.