Not quite the same as your issue, but we had a downspout that was flooding our side yard/berm. So we routed the water by building a dry creek bed…pretty easy DIY, and not expensive at all. Dug a small trench, lined it with landscape fabric, laid down some gravel, then some larger rocks. Then we lined the edges with some larger stones…which made it look nicer, and also keeps us from running over the area accidentally with the lawnmower.