Despite what you may have read or heard - No, it doesn't rain all the time on Yakushima. The 35 days of rain a month quote that people like to use just doesn't represent reality.
Don't believe me? Check out Is it going to rain in Yakushima on my trip?
Around the coast there is as much sun as there are rain clouds and depending on the season there could go several weeks of droplet free, clear skies. When it does rain however - it pours down with a vengeance but only usually during rainy season in June/July.
The big difference in the weather in Yakushima is that between the coast and the mountains. Look at this weather forecast for this week on the coast.
And now look at the same weather forecast for the high mountains.
For visiting in the winter visit Snowfall on Yakushima