to find the center of a dowel, make a jig that is square and the dowel fits into.

a 3/4 inch dowel would require a 3/4inch square hole in the cenetr of your jig. then just connect the corners of the square diagonallly over the dowel. it should cross directly over the center.

make it long enough that you have extra, and drill through your jig into the dowel. any drywall screw will do. that will keep it from turning in the jig.

USING YOUR drill press, and drill press vise, drill stright down the ceneter of the dowel.

or since you dont have press, place the jig in a vise or clamp it to a table. and eyeball it. you might try a 1 inch doewl to giv you some fudge room, or just use a piece of PVC tubeing instead of the dowel.

just be sure not to hit the screw with the bit.