La Fortuna is wet year-round — it sits on the Caribbean slope where rainfall is heavy even by Costa Rican standards. The least rainy months are February, March, and April. The green season (May to November) brings heavy afternoon and evening rains but often clear mornings, which is exactly what you want for volcano views. December and January are transitional.
The volcano is most likely to be visible in the early morning before cloud builds around the summit. Arrive the evening before any planned activity and try to do the key things — waterfall, lava field hike, hot springs — in the first half of the day. Rain gear is essential regardless of when you visit.