You are supposed to use a reamer like the ones you can find on www.lmii.com but you don't really need to spend that kind of money on a reamer. Just get a drill bit that is about the same size as the whole in there and then wiggle it around in the whole. Do it untill its big enough to get your tuner in.
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If you decide you simply must use a twist drill on it, clamp a sacrificial piece of wood on the back of the headstock to allow the drill to enter that piece of wood as it exits the peghead. This prevents chunks tearing out as the drill exits. Use a drill press preferably. It works just fine. I just did this on an Allparts neck to fit some Sperzel tuners.

read up here. I've retrofitted all my guitars with Grovers...and most required reaming. I suggest you don't use a drill, since a drill bit may or may not follow the old hole's placement exactly...having an unsightly hole on your guitar head is not cool!

And...reamers are cheap (like $5), I found mine in the plumbing department in my local OSH.
-Epiphone Riviera w/ Bigsby and Gibson 490r/498t combo
-Epiphone Es-333 Delonge Edition
-Fender Twin Reverb '65
Thanks guys.
Quote by Kanthras
Since there is no such thing as perfect tone, and every rig has differences (however slight they may be), I hereby declare this claim as bullshit.