The phrase "God willing."

Does "God willing" have a religious connotation to it? What are some other phrases that mean the same thing but don't have this connotation?

"God willing" means "If God allows this to be so," so it has a religious connotations.
Other phrases that do not have religious connotation include "If Fate decrees", and "If the wind blows right", or "Hope its my lucky day", all of which relates to the future, but does not have the religious connotation "God willing" has.

How about the expression knock on wood.¹

One of the origins for the phrase "God Willing" or the Latin deo volente is in the Bible from the letter of James 4:14-15

¹⁴ Yet you do not even know what tomorrow will bring. What is your life? For you are a mist that appears for a little while and then vanishes. ¹⁵ Instead you ought to say, “If the Lord wishes, we will live and do this or that.”

The phrase "God willing" is of the type of phrases that are added so that the speaker does not jinx their good luck by speaking to freely about it.

So, equivalent godless phrases are other kinds of protective magic against the envy of demons (like knocking on wood).

I don't know if there are many people who want to avoid using a religious phrase, but need to protect against demons, though.