Hi Johan, I like to use punched foil if possible because it's much faster and generally gives much more uniform results, but as you say some punch-and-die sets don't go small enough! If you have never tried it you can punch foil using the bottom of a drill bit, if you have any very small bits you might be able to make some smaller than your set can make.
The obvious way of forming small round shapes with putty is to use a small tube to press in the shape to a thin layer of putty, you then trim away the excess carefully with a needle or other tools. You may be able to find hypodermic needles of the right gauge for the size of button you want but once you go very small I've found it's nearly impossible to get the putty not to stick to the tool and come away from the surface although it can work better with Kneadatite.
For very tiny buttons or rivets that I can't make using foil or by pressing I now generally 'dot' these in from a paste of MagicSculp - you mix a fresh batch of MS and put a drop of water on it, leave it for a few minutes to be absorbed by the putty which you can then stir a little to about the consistency of toothpaste. You pick up a little bit of this with the end of a sharp tool or paintbrush and just touch it carefully where you want the button/rivet to go. It's usually fairly easy to make them round but getting them to be consistent in size is tricky so be prepared to wipe off and start again, and again...! They are quite fragile when fresh so be careful if you're doing more than one at a time but once the putty has cured they are surprisingly tough.
Einion