When I drill for barrel pins or rod pipe pins when the stock has been fully shaped, I make sure the layout for their location is perfect, marked with a fine tipped pencil. I then prick punch the locations with a thin punch quite deeply (1/16" or so). I set up the stock with barrel in the channel, using the top flat to make sure the gun is held square and level. I use 1/16" pins so I install a sharp 1/16" drill bit in the press and set the speed to highest setting.
With the gun in the vise and the vise clamped solidly to the table in the exact location for the pin, and the drill press running, I bring the bit down until it just touches the pin punched mark and hold it there while it begins the hole. Now I continue down slowly about 1/14" and clear the chips. Now the bit is exactly where it needs to be, and I continue to drill all the way through, wood and lug. Drill a little, clear the chips and continue. It's quite easy to do. Be patient and precise.