I used to make clocks and misplaced holes in plates are not uncommon. The rule is never to scrap off the plate. Here's a simple technique that works with most metals;

1. Lightly countersink each side of the hole - I use a hand countersink
2. Select a piece of rod of the same (or similar) material to the parent. It needs to be a good, preferably tight fit.
3. Cut it so that it projects 1/2 the diameter on each side.
4. Rivet over, working from each side.
5. Cut a small hole in a piece of acetate film and locate this over the rivet 'head'.
6. Use a riffler or preferably a bulls-foot file to remove the surplus rivet material - the acetate prevents damage to the surrounding metal.
7. Finish smooth with abrasive papers, making sure the grain and surface texture matches the parent.

Sounds involved, but takes just a few minutes to do. The rivet swells into a barrel shape and along with the countersinking locks it in place. This technique is centuries old. I was explaining it to a customer about two weeks ago and showed him a clock I'd made with incorrect hole spacing for some wheels, except neither of us could see where the holes had been plugged.

Practice on some scrap to get the feel.