Center drilling dowels can be one of the most frustrating tasks a woodworker can take on in his or her shop. I once spent several hours wasting many pieces of dowel trying to get an exact center. I finally gave up, which is sometimes the best thing to do when getting tired and frustrated and working with power tools.
The next day this simple solution came to me: drill a large hole in a block of wood to hold the biggest dowel, insert the big dowel in the large hole without changing the position of the initially drilled block, change the drill bit to the size of the smaller dowel, and drill the small hole.
I tried this technique several times with several different dowel sizes with some only an eighth of an inch different in diameter. Each size worked perfectly and most importantly safely and without any frustration.