How far is the greenhouse from any AC source? I'd just short an ATX PSU and use that so you never have to worry about recharging. If the moisture ever gets to the PSU you can replace it. You could probably find cheap 150~200W units. Alternatively you could look for laptop power bricks or power bricks in general. Being sealed they'd fair better in the heat/humidity.

@Windows7ge

No AC, just solar.

That should work just as well.