Make a jig deep enough to rest against the riser behind the tread out of a 1-foot-long piece of 1-by-10-inch piece of board. Cut a semi-circle into it with a jigsaw so it supports your router in position along the edge of the tread. Sand the jig so it doesn’t catch or bump as it moves.
Cover the inside of both stringers along the tops of each riser around its edge and a few inches down the stringer underneath with painter’s tape. This may not protect the wood if you make a mistake, but its bright blue shred will warn you to stop.
Choose a bullnose or half-round bit for your hand router that has a diameter equal to the depth of your stair tread and put it in the router. Put the router in the jig, turn it on and take one pass along the edge of the tread. The jig should stop the router several inches before the bit or hood reaches the corner.
Check the tread edge to ensure that the cut is what you like. Adjust your jig if necessary and run the router lightly along each tread two or more times to achieve a smooth bullnose profile. Create the bullnose at the ends of the treads where the router can’t reach with a utility knife and flat or corner-clearing chisels.
Sand the finished edges until they are smooth enough to take stain and varnish.
Sand each tread surface, vacuum up all the sawdust and wipe the entire tread with a tack cloth before finishing.