Go to your local building supply store and ask at the pro desk. I don't mean home depot or a landscape yard but rather a place that specializes in brick and stone construction materials

With my limited experience I would say to use mortar assisted by a bonding agent and use the smaller trowel teeth to apply. Thin-set may work as well. Problem with only doing the "up part" is that your joint will be exposed at the top, directly where moisture will sit. Thus I recommend a very clean joint and apply a sealer over that strip and don't forget to reseal every couple years or so.

FYI- up and down part=riser, where you step part= tread