I have a Johnson Scotch and Soda kit, which I like. I added a few more Centavos which are fun to use with this trick as well.

When I attempt to add a quarter under the "Soda" coin and then attempt to place it in a hand, I get noise from the quarter. It immediately gives a tell that something isn't right, because it should look like, and sound like I am only placing 1 coin in the hand.

When I place the "Scotch" coin under the "Soda" coin (which is actually placed above the hidden quarter) I am fine with the coins talking, as that makes sense as you place one coin under another.

How can I get the quarter to be perfectly silent as I initially place it under the "Soda" coin, and then especially when I place it into a hand (either my own, or a spectators / participants hand)?

Maybe a thin piece of tape on the underside of the "Soda" coin? Is there enough clearance for the "Scotch" coin to seat properly if I do that?

I think you are over thinking this.

If you talk OVER the little bit of noise, they won't hear it.

And get eye contact with them for a moment.

Audience management. You get them to focus where you want them to focus and when you want them to focus.

Arther Emerson use to call it "sleight of mouth."

If you want to investigate the tape idea, buy a roll of optically clear teflon tape https://www.amazon.com/CS-Hyde-Optically......00REI90W

Very think, totally clear and it is so thin that you shouldn't have problems with adding thickness to the coin.

You could also place tape on the quarter. It's not great for examination, but you have the same problem if you want to hand out the closed S&S for examination.

But I agree with Al that there are simpler ways to mask the slight sound.

I contacted Johnsons to see if they had a solution, and they simply said they didn't.

I did a little more research, and found an out of stock possible option on Penguin Magics website. They are Teflon circles with an adhesive backing made by Roy Kueppers, in a two pack. I searched the Internet to find them in stock somewhere, but no luck. Since Roy is currently crafting a walking Liberty shell set for me, I asked him about these, and he kindly agreed to throw one in with my order.

I think I still need to work on the technique, and as mentioned, how to use patter and focus to make the delivery solid enough to ensure a successful presentation. I think those things, combined with the Teflon disc, will produce what I am looking for.

Great suggestion on the effect. Sound issue has always been a concern.
Definitely going try it out. Now I can perform the same trick in libraries and quite environment.

I always put both coins in the spectators hands, nesting the coins together as I ask them to hold out their hand, so that the smaller coin is on the bottom. I then ask for them to pull out the larger of the two coins. I say, you gave that one to me willingly...blah blah blah, miracle.

Maybe that will work for you instead?