Pretty sure the standard spindle diameter is 9/32". You can get a 9/32" bit at most any hardware store.
Spindle Holes
I'm noticing with a lot of new vinyl that the spindle hole is too snug, not only on my turntable but also on my RCM. I had a bit of a mishap earlier this week, and I was wondering what people are doing to counteract this problem. I don't recall it being the case 30-40 years ago when I started in vinyl, so I wonder why is it happening now. Why can't the vinyl producers get the spindle holes slightly wider?