Shoot, I wrote a big old long answer and it's gone. I even tried copying and pasting, but it didn't work UGH!
You obviously care about this little boy, and if I were in the same position, I don't know how I could keep quiet! Without actually being in your situation, I feel like the boy's well-being is worth more than a few hurt feelings.
Unfortunately, my friend WAS in this position. She (a nurse) and her mom (who watched the boy at her in-home daycare) both suspected autism. She is very conscientious, so I imagine that she said it very tactfully, but her friend was supremely offended and hasn't spoken to them since. It's been about 8 years. She's so sad for losing a friend, and even worse, she doesn't know if her friend ever got her son evaluated, so she doesn't know if it was even worth it!
I think I would bring it up very gently. Some time when you're there with your friend and her son, you could say, "Have you noticed how he ______?" See what she says. If she seems open-minded, suggest that she ask her pediatrician about it. If not, keep your mouth shut for a few days or even weeks. Then bring up a different concerning behavior in the same way and suggest she ask her doctor about it. If she gets defensive or asks you why you're talking about this, you could say, "I don't know, maybe I'm just paranoid because a kid I used to nanny turned out to be autistic."
I'm sorry that you've gotten some nasty responses. There's no place for that. You obviously care about your friend and her son. Unfortunately, I worry that your friend will react like some of these women, immediately getting offended and closing their mind to the possibility that her son isn't perfect. Good luck!
I read through a few more responses, and had to add that if your friend already suspects, then she'll likely be open to discussing it. If she already knows, but just isn't broadcasting it, then she'll likely talk to you about it. So why would you keep your mouth shut on the off-chance that she knows?