You need to use a penknife blade to ease them out. If that fails, run a blade round the hole until it gets big enough for the ball to pop out and then I have used a tap screwed in a couple of turns to pull the remains out. These button oilers come in metric and inch sizes, you have to measure the hole. The Tom Senior mill had three sizes on it.
Steve's self tapper is a good method.
Edited By old mart on 27/12/2020 14:44:57