One is to take the smallest drill bit you have - like the size of a fat needle, and make a pilot hole in the rivet first, then switch to thicker bit to finish it up - the pilot hole will help keep the bit in place..

The other idea is one I just looked up, which might not be doable in your situation.. Put a small piece of painter's tape (the blue tape) or any kind of non-shiny tape over the rivet.. hopefully the tape will give the bit something to dig into and help keep in place..

Normally, traditionally you'd start the drill slowly, but from wha tI've read, that's what causes the drill bit to start "walking" away from the spot you wanna drill.. so they say go in fast... I've done that, but if it slips, you may have a hole somewhere else that you don't want it..

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