I purchased an Aurora Solar Charger for my sl5600 about a year ago. When it was working it did charge the Z. However, a pin on the adapter broke and that had to be replaced before it would start working again. Fortunately, a friend was able to make the simple repair for me with the purchase of a new adapter from Radio Shack. There was some question of the pinouts but he resolved it (which is hot which is ground).
It's not fast, but it works.