I just found out that "snapshot" is more of a term regarding quick picture taking, usually without much artistic intent. But we do want to sell our artistic aspect. I agree that the word "click" does remind people of something related to the mouse instead of a camera. But in some ways, it can also suggest that the customers are clicking into our website to view our works, which is one step closer to having us capturing their precious memories. So it may also serve as a pun. What do you guys think?

I may now change it to something like:

#1 Creating Precious Memories ... Capture one at a time

#2 Creating Precious Memories ... One Capture at a time

#3 Capturing Precious Memories ... One Click at a time

#4 Keeping Precious Memories ... One Capture at a time

Anyways, thank you so much for all the inputs. You guys seriously help me a lot in making this slogan. This is fun too.

Capturing Precious Memories...One Click At A Time

Whatever you choose, they all sound great. Best wishes!

You could use
"One image at a time"
"One picture at a time"
"One smile at a time"
"One shot at a time"

I like #3 Capturing Precious Memories ... One Click at a time.

These may not be what you're looking for but what about these:
Memorable Moments... One click at a time
Forever Keepsakes...One click at a time
Beautiful Expressions...One picture at a time
A moment in time...one image at a time

or:
Capturing life's memorable moments...one picture at a time

A Time To Shine...A Click At A Time

capture the moment - a moment in time