Best one I've seen is: "I'll think for you". A little snarky, yes, but it does get the point across.

I all was use the saying I am sending good thoughts and best wishes for the best outcome.

I usually say I am sending good thoughts your way. I do this because I believe on a Quantum level we are all connected. And when positive thoughts, from many people, during a certain time frame,are made, they very well may have some effect on outcome. It is science based not spiritual based.

"I wish you the very best." "Take responsibility for yourself." Okay, maybe not .

I used to be Pagan so if they are long distance I just say "sending positive thoughts your way". Otherwise, I offer to help if needed. Never had anyone turn down positive thoughts.

"I'll keep you in my thoughts"
"I wish you the best"

" I'll be wishing the best for you. "

The past few years I've been saying 'Sending you peace and strength', but am thinking now that its way to close to the uselessness of 'thoughts and prayers'. Anybody?

In similar situations, I have bought a large amount of good liquor for them to salve their pain. It works when all words tend to ring hollow.

"I hope things get better.". Also "I'm sorry you are going through this".

You're right, no sincere words would fit. What is right, and what might bring solace, is to just listen and hold their hand.

I have an advantage of being an atheist for more than sixty years.
If they ask, "will you pray with me?" I say, "no, but I'll listen to yours."

When my 18-year-old daughter died I was very offended by stupid things people said to me such as "She is with God" or "You can have another baby." Just being there to listen is essential. Hugging can upset the grieving person so pay attention to their behavior. Doing something for the person is nice but merely being there and listening is the best thing as no one wants to be shrugged off or told something inane.

You can't go wrong with a sincere I'm sorry.

I can understand as I have been on both sides, close family death and friends becoming gravely ill and or die unexpectedly. There is no clear answer. I usually go with I am so sorry. Then I try to be available if they need to talk further.

I say "Sending good vibes your way".

I hear my fellow Christians say "I'll pray for you" all the time, and I have to wonder if they really do? Do they just say it to be "polite" and then forget about it and go to lunch?

Instead of telling someone that, I ask them if there is anything I can DO to help - what do they need NOW? Can they use an errand runner to the grocery store or pharmacist? Money? Or just an ear? Or someone to call at 3am? They don't need to know I'm praying for them, and most people really prefer/need hands-on help at the moment.

Replacement? No idea.
Response? Thank you.

I'm the same way. I've never found a good replacement, either.

"I'll be thinking of you...let me know if there is anything I can do to help."

"I need the prayers and you need the practice"..................welcome to Waco

Well if I cared about the person I ask is there a way I could help. Unfortunately under the circumstances of this situation I probably would have handled it differently.

I just tell them the truth of what I want to express: I mention first that I am clumsy with my words sometimes. I tell them that I want to let them know that I feel horrible for what they are dealing with. I just show up to do stuff, like dishes,, housework, gardening, lawn, etc. It is easier for me to do actions, instead of talking.

Since I believe that "praying for" someone does absolutely nothing at all to help or better the situation in any way, I guess my equivalent would be to do nothing at all or help in any way to better the situation.
But if the phrase is being used by someone who truly believes that prayer is a way to provide comfort and assistance, I suppose my equivalent (depending on how much I like the person in need) is to offer my heart and home to them and let them know I understand struggle and will remain available whenever they need a good cry or cold beer.

In a case like this, I would just go along with the request for prayers. It is not important for me to ALWAYS blurt out my atheism. It is sometimes better to be kind than to be bluntly honest. In a time like this, I will say anything to help a person feel a bit better.

I say I am sending positive thoughts and energy your way.

Some variation of "I wish you the best, let me know if I can help you" usually works for me.