Wide rim rivets like the 1/2 inchers or bigger. Dry punch the rivet then use a nail the size the brad would be and length. Trim the rivet so all you have is the collar left. Over the open jaw in a vise ram the nail through the rivet. Then use the vise to squeeze the new button back through the material and into the button head. They will bend sometimes so the vise will give you more control when you are putting them together. The nail will lock in and then the head will hold the rivet on all sammiched together.
This will work for a long time but they will spin. Just check them from time to time and see if you need to use a channel lock to reset everything together again. One guy I showed this to said they dug in, so he would wrap the rivet nail head in felt and pull the ends back over and put that over the nail before squeezing and he said that helped and held the felt until it wore off. Personally I think he was a little less than stellar in the masculine department.
Owl