"Wish you well"
"You're in my thoughts"
"I care about you"
"I'm here to support you"

"Peace to you. "

Yes. As noted, "best wishes," "good luck" and other equivalents serve the same purpose ... and are equally unefficacious as "I'll pray for you."
They really serve just to indicate your attitude of sympathy, support, etc. toward the person.

Your in my thoughts.

I often reply, "Thanks for thinking of me". After all, giving attention to someone can be a loving thing. The opposite of love is not hate, it is indifference.

It might be a little snarky, but I always say I will cast a +10 spell of healing and mana regain. They never think that's funny

Listen empathetically, offer support, use a similar ecperience of your own to relate, ask what you can do to help.

Sending positive thoughts your way.

"I don't actually give a shit about you but I'm going to pretend I do"
or
"nothing"
because thats what they actually do.

In this case...I believe "I am here for you if you need me" would work. In most cases where I will pray for you is needed I would either keep silent or " I will think about the problem and see if I can DO something to help"

Say "I'll be hoping for the best/for his or her recovery/for peace and comfort...."

How about, I'll see what I can do

Yes, it might be inconsiderate to point out to your co-worker at that moment that if prayer worked, his child would not be sick. If prayer worked, we would not need doctors of any kind, hospitals, insurance agents, tornado shelters, counselors, mental health clinics, etc., etc., etc. In that situation, I might say, "I am so sorry that your family is suffering. Here's my number. Call me whenever you want to talk."

If I can do anything to help, please let me know.

"Destiny be with you."

I usually just say "keeping a good thought for you". Seems to do the trick. If anyone wants more, I'm fresh out.

"How can I help?" is the closest thing to what a believer seems to be driving at with "I'll pray for you." It's risky though, because you may be asked for something you are unable or unwilling to give. If you can offer something specific, like, "Call me any time if you need someone to talk to," that seems more helpful than a promise of prayers, but you must be prepared to take the calls.

My heart goes out to you. Sincerely.

I believe in you or my thoughts are with you.
Also whenever a christian fails at trying to convert me with some I feel no remorse cause of thier negative attitude, but others with good intentions that get overly stressed out I found that telling them "I'm sorry you feel that way." Usually changes the expression on their face and puts them at ease. Please don't be dicks to those that have good intentions other don't have a problem with starting a war but like us some of them just want peace

"I'll think for you." Lolz! Seriously though, I just say I hope everything goes well and let them know I'm available for whatever they need.

I tell people "I wish you well", also Christmas is a huge issue for me. When someone says Merry Christmas my return is "happy Santa Claus day"

I never say "God bless you" or "I'll pray for you", because deep down, I don't really believe it, and I don't want to lie to anyone. I usually say "I'll keep you in my thoughts", which people take the same way (I think), and I usually do give some thought later on to the situation the person is battling. I can be sympathetic or compassionate without invoking the will of anyone's god that I don't believe in.

Silvereyes, you handled that beautifully. I had a career as a counselor, and I don't believe I could have done better.

"I'll send good vibes your way."

I think that seems about right. It's kinda along the metaphysical line of spiritual thinking, and it can also be backed up by science. There's studies that show that everything is connected, water somehow reacts to our emotions, and of course there's the whole quantum tunneling physics that throws a loop into people's worldviews who think that everything is separate. We are one.

I always say “ I wish you well” instead of “ I will pray for you”.