SIM908 Li-Ion charging with 6V solar panel
The answer is to use a charging chip that has the ability to back off on charging current when the input voltage from the solar panel begins to collapse.

While using a regular Li-Ion charging IC will technically "work" with a solar panel, it will take forever to charge in practice, and, as mkeith pointed out: "it will never get a chance to terminate charging".

The discussion about this on the Adafruit website is the best explanation of this phenomenon that I can recommend to others with this question:


  Most people try to plug a solar panel directly into a lipo charger and while it sort of works, the battery takes forever to charge because the efficiency is terrible! That's because most lipo chargers are meant to plug into a USB port or wall, and are very simple in their design. USB ports supply 5V at up to 500mA and they're pretty solid - the voltage doesn't change much even at the max current draw. So when you plug a charger into a computer with a USB port, they just draw 500mA or so and happily chug away. Same goes for wall adapters. The voltage and current limits are kept steady.
  Solar panels are a little different, the voltage and current vary constantly depending on sunlight available. They are unstable! That instability confuses battery chargers, which causes them to do one of two things: rapidly turn on and off as they try to draw more current from the panel than possible and/or draw much less current than they can, to keep the voltage from collapsing