I think that's probably a decent way of handling the situation. "Prayer isn't my way, but I'm very glad for you and your son and your whole family that he made it through that scary experience. If you don't mind, I'd like to finish up my shopping and get home to my own family. Have a good one!"

It seems you dealt with it well. I would recommend the "Street Epistemologist" channel on YT. or Peter Boghossian's - "A Manual for Creating Atheists". Mostly try to stay pleasant & questioning, not confrontational. Now, if you come up against a Ken Ham or a Ray Comfort, all bets are off!! Just be sure to stay on ground you're familiar with, they love to twist things!

I find letting folks get to know me and my values and morals as a person over a period of time and then revealing mylack of religion leaves some shocked, but rethinking their views of us as immoral evil people.

There are many people in the world who just will never get it. Don't waste too much time and effort trying to reach people who can't or just don't get it.

Sorry not interested is what I say.

A couple of thoughts here. One, the man was in pain with his son's condition and was trying to find some ease in his religion - maybe hoping that you would share his views and talk with him, agree with him, boost up his hopes of prayer giving back health or life to his boy. Second, he was in no condition to talk about a change in his views. He needed/wanted comfort and assurance that all was going to be fine since he Believed and had been Saved.
There was nothing you could do to help this man. If you had been a committed Christian, you would have said all the right words. In his heart, this man really knew the truth of his situation, but was trying to force this promise from Jesus that said something like --whatever you ask in my name will be granted--.
I am sorry for the man that talking totally different ideas from what he wanted could not console him. Having lost a son, I can feel his pain.

They need more mental help.

Faith denies proof, these people are more than close minded.

You don't change people with one conversation. If you somehow made them realize just a little bit, that non-believers aren't ogres you did good.

Hi there. I like to stick to the adage that advice should only be given when asked for. People are more open to discussion and shared ideas when we're not ramming our beliefs down their throats. Doesn't help when people are thrusting pamphlets your way, and in this case the added element of emotion associated with family sickness probably meant you had to tread carefully. Not easy to respond to the "I'm worried for you" statement either, at any time. I'd have asked them if they have any experience of socio-cultural evolution and the predictability of superstition within any given phenotypical group. Then they'd have moved on. They usually do!

Ugh I hate Bible humpers. While I tend to let it go with people who are going through grief ( I am not sure, if the kid in question died or survived and in remission), and generally don't start the conversation. I tend to say "No, thanks" and walk away, no explanations needed.
However, if the conversation does occur, and depending oh what level of holier-than-thou is thrown in my direction, my first response to someone like this would be "Why are you worshipping a god who gave your child a deadly disease? Should I thank a person who mutilated me? Should I stay in a marriage with someone who tells me to love them, or I will burn in hell for eternity?" or a variation thereof. It does seem rude and cruel, but the attitude of "I will pray for you, bless your heart" is already rude, and I am done being complacent with assholes. Generally though, conversations like this don't lead anywhere productive anyways. If I engage in a debate about beliefs or religion, it's only with people who are open to another point of view.

To put it simply if their mind is so full of belief in a divine being or whatever then any attempt to convince them otherwise is likely to fall on deaf ears. Taking a rigid stance is likely to reinforce their beliefs.

How can I pour water into a glass that is already full?