Following this article, it looks like one has been developed by LG already:
Designed by LG Display, the sleek reader features a wafer-fin
photovoltaic cell that provides it with a steady stream of solar
Read more: LG Unveils Solar Powered E-Book Reader | Inhabitat -
Sustainable Design Innovation, Eco Architecture, Green Building
It seems that there is one in development in Finland: Article.
A new Color e-Reader is being developed by five media companies based
in Finland. Their intention is to offer a low cost device that can be
charged via solar power and used primarily for the consumption of
newspapers. There is a beta test beginning in November that will see
SolarMio provide integrated solar panels into their lighted cases for Kindle 4 and Kindle Touch devices. I bought 2 of their cases for the Kindle 4 in spring 2013 and they seem to be working well in Kenya where they're deployed with Kindles.
http://www.solarmio.com/en/4712389290366.aspx (Kindle Touch)
http://www.solarmio.com/en/4712389290168.aspx (Kindle 4)...