Center that peep with the housing of your sight. It will make you more consistant than trying to center a little dot in the middle of circle. First thing I always do when setting up a bow is get my draw length just right, then get my anchor perfectly comfortable. Then everything else just falls into place.

If you can, try moving your sight out more to get the housing inside the peep. I use a Fletcher super hunter at 3/16" and an Extreme Sniper sight and they line up perfectly. I used to use a Copper John, but the housing was too big for me and I couldn't get everything inside the peep.