What I'm wondering about is how thick a coin can be and still be shipped in a thin envelope and pay the lowest First Class fee. For instance, it would only cost 55¢ to mail a few dimes or pennies wrapped in a bit of thin-foam padding. But I'm not sure about nickels or quarters. At the post office, they said that the limit is 1/4" (and it needs to be bendable), but I've used the package rate (somewhat under $3) to mail half dollars and 1-oz silver rounds. I haven't mailed anything smaller yet.
I have shipped nickels and quarter sized coin in flip or paper 2 x 2 with no problem, packaging it as you describe, and normal 50 cent stamp.
You can also ship international for $1.15 I think.
Next step up for me is to attach the coin (in a flip or 2 x 2) between two pieces of thin cardboard (half dollars, but I have also shipped some "Blue Ikes" this way with another small amount of postage, as these go over 1 ounce). If under 1 oz., you buy a 72 cent stamp and get it hand cancelled by the clerk, or write "NON-MACHINABLE" in red ink (same as their red hand-stamp), and put it through the slot..
If your postal clerk is "by the book" they will measure the thickness, but they can't if you just drop it in the slot.
But remember if the customer files an INR, you are screwed and have no recourse. I don;t know my exact loss rate, but it is on the order of 1 out of 100. Maybe I'm lucky.
how much would it be to ship a single coin in a carboard 2x2?
I don't do it for pennies, nickels or dimes I always take the coin out and re-package into something thinner. The size and thickness of the 2 x 2 can only cause problems if you are going to mail at basic first class rate. I have sold a few lower value quarters the same way, and shipped some better ones in their 2 x 2 between cardboard as I described above.