The dry season — December through March — is the only realistic time to visit Sapo. River crossings are easier, the trails are passable, and wildlife concentrates around remaining water sources, which improves the (already slim) chance of sightings.
The rainy season runs from May through October, and at its peak (August–September) trekking inside the park becomes very difficult — game trails turn to mud, rivers run high and often unfordable, and the access roads to Greenville and Juarzon become impassable for ordinary vehicles. Even in the dry season expect afternoon showers and high humidity; this is equatorial rainforest, after all.