Miyako has a subtropical climate — warm all year, with most rain falling between May and September during the typhoon season. Typhoons are a real risk from June through October, and one can cancel flights and close beaches with little warning. The island is small enough that a direct hit is genuinely disruptive.
The best time to visit is March through May: the sea is warm enough for swimming (around 23°C), the crowds are manageable outside the Golden Week holidays in late April and early May, and the light is exceptional. October and November are also good — water temperatures are still comfortable, typhoon risk is dropping, and the Paantu festival takes place somewhere in this window. The All-Japan Triathlon in April brings a significant crowd and fills accommodation — book early if you're going then.
Winter (December to February) is mild by Japanese standards — temperatures rarely drop below 18°C — but the water is cool for swimming and the island is at its quietest.