Thank you all for your very helpful replies,I've only been an,announced agnostic for a short time, I intend to study and will embrace agnosticism even more!

Thank you all again,

You might learn about their affliction. Then you could discuss things with them. Relate better.

I say, ‘let me know if I can help’. Simple. True. Understood.

Show empathy.

Just let them know you care. No mention of religion of god is necessary to show compassion.

I had a customer tell me that her dog was not doing well the other day. Rather than "I'll keep them in my thoughts or prayers" I went with "I hope for the best." Its a simple substitute that still shows concern.

Make time to be with them, listen, talk with them and enjoy being together. Help them when you can.

Through action. Donations, charity work, whatever. Just don't sit on your backside with "thoughts and prayers" or the equivalent BS.

"You're in my thoughts" is the secular equivalent of "I'm praying for you," at least in terms of practical effect. But I think if you want a connection ask about things you know are important (kids, work, doctor visits, etc.) And learn what their needs are. Then you can offer up some of your time for specific things (e.g., provide travel to the Thursday appointment each week, or provide evening childcare a couple of evenings each week, or on an especially busy day help out with meal preparation). There is far more value in actively helping, or even in routine visits, than in uttering platitudes. I hope you find a way to help and provide comfort, and that your relative recovers soon (or at least isn't in any severe pain).