The RRT4 Rivet Removal Tool is great for drilling out solid or pull rivets with a button head. The included nosepieces center the drill over the rivet to align the drill bit.
Tools mentioned in this video

RRT4 Tool Kit: http://www.cleavelandtool.com/RivetR...
Drive pin punch (1/8"): http://www.cleavelandtool.com/1_8Dri...
Drive pin punch (3/32"): http://www.cleavelandtool.com/3_32Dr...