What kind of battery does it use? I thought I remembered reading it was a NiMH battery pack? This link seems to corroborate that:
If it's a 12V lead-acid battery, I would be comfortable putting a 12V lead-acid trickle charger on it. But I suspect that most of the solar-powered chargers are for lead-acid batteries, not NiMH.
If you can find a solar trickle charger that's specifically for NiMH batteries, great. But if not, I would use the plug-in charger.