Rose,
Letting it soak in would have to make it more effective. I always get impatient and wipe right away! And, I've never thought of using fresh coffee. That might work better too.
I think I may have initially read it in some list of things you could do with old coffee grounds. I'm pretty sure that there was something in there about using it for your plants?
I don't see why tea wouldn't work just as well if the wood is a light color. That would also give you a light, natural stain.
My favorite use for wet tea bags is to stop bleeding. We use them if we accidentally clip the dogs nails too close, but an oral surgeon also recommended them recently for light post-extraction bleeding.
Maybe this post will turn into everyone's favorite tips for using coffee/tea in new ways? That would be pretty cool!
For your original problem, check a home improvement store like Lowes or Home Depot for a scratch repair pen. I haven't used one, but they say they'll fill the scratch in to make it smooth - and they may even have them in a variety of tones to match the wooden surface. I know they have them in clear polyurethane to put the shine back and make it less noticable. Should be an under $10 fix.
A strategically placed plant or decorative item works too.