Just my 2 cents. I always drill with my lathe. I use a 3/16, 6" long brad tip aircraft drill bit. I bought this plastic template at Woodworkers Warehouse that enables me to find the center in any stock round or square.
I drill from both sides and rarely miss. When I am off a bit I can usually re-drill and compensate. The trick is to back off every so often to allow the flutes in the bit to clean themselves. I don't know if that makes sense but the bits tend to wander or walk when the get full of wood. Kinda like chipping away at the hole.
