The Kona coast is one of the driest parts of Hawaii — the leeward side of the island is sheltered from the trade winds that drench the Hilo side. Temperatures stay between 24 and 30°C year-round, and rain is rare. Any time is a reasonable time to visit.
The main events worth timing a trip around are the Ironman World Championship in October, when the town fills with athletes and spectators, and the Kona Coffee Cultural Festival in November. The Ironman is impressive to watch but accommodation prices spike and everything books out months ahead. If you want a quieter visit, April–June and September are the sweet spots: weather is good, prices are reasonable, and the mantas are out year-round.