If they're fairly short, you could make a v block jig and drive it with a drill, and use a chisel on the side you want to round over. There's a vid/gif I saw recently of a gentleman doing it to make the dowels themselves after knocking the corners down with a hand plane
Could you use a jig to hold the piece vertically and clamp to keep from rotating, with the to be rounded part pointing down and a router table with roundover bit?
I was thinking horizontally. I'd hesitate to do it vertically since gravity would be pulling the stock into the bit. If anything went wrong it's not exactly fail-safe.
I think the roundover bit is your best bet. But you don't have to go vertical. Horizontal, perpendicular to the fence of a router table. You will need to build a jig somehow.
A 1/2" dowel might fit in the shank of a standard hand drill... If so, I'd use the dowel in the hand drill and would round off the other end against a belt or oscillating sander, basically.