Manihiki sits in the tropical South Pacific at around 10 degrees south, which means it is warm year-round. The dry season runs roughly from May to October, with lower humidity and less rain — this is the more comfortable time to visit. The wet season from November to April brings heavier rain and higher temperatures, and this is also cyclone season. Cyclone Martin, which devastated the atoll in November 1997, is a reminder that the northern Cook Islands sit within the cyclone belt.
The best lagoon conditions for snorkelling and diving tend to be in the dry season when winds are lighter and the water is calmer. For pearl farm visits, timing is less critical — the farms operate year-round, though harvests happen at specific intervals and visiting during a harvest (if you can arrange it) is a genuine spectacle.
Given the irregular flight schedule, the best approach is to fix your travel dates around what Air Rarotonga can offer rather than around any seasonal ideal. Flexibility is more useful than timing.