There are several ways to find the center of a dowel, but I want to do it quick, painless, and for free.
Step 1: Glue Up the Square
I've seen these made as triangles and other shapes, but they are always flat and have to be balanced on the end of the dowel. I had 120 dowel centers to mark for game pieces and I didn't want that aggravation.
I started with two pieces of scrap 1/2" birch plywood. Let's call them 2 1/2" x 8" and 1 3/4" x 8. The 3/4" piece in this picture is just for a larger clamping surface.
Step 2: Reinforce the Angle
This step probably isn't necessary, but I thought maybe if I overlapped the first butt joint with a layer of hardboard, it would help keep it square. I used hardboard because it is stable, affordable, I always have it, and I use it on most of my jigs. I left the hardboard long, glued square to the corner and then just trimmed everything up on the table saw and miter saw once the glue dried.
You can't see the joints very well, so I made a quick sketch. I'm at the bottom there with my messy hair, scribble beard, and four misplaced tape measures. I also need to lift weights by the look of my arms.
Step 3: Add the Triangle
Last step is to add the triangle to one end. I just took a length of 2 1/2" wide hardboard to the miter saw and cut the angle, left it long, glued and brad nailed it (with attention to alignment), and then trimmed it up once dry.
Step 4: Mark the Center
The dowel is easily supported and squares to the corner of the jig with one handed operation. Mark your line, rotate the dowel, mark a second line - done.
It works with small square stock as well so you don't have to mess with a ruler and two lines corner to corner. Also works for small lids and cans (my mini percussion shaker for instance).