The climate of Miyako-jima is sub-tropical, with very mild winters, and long, moist and rainy summers.
Miyako-jima is the most important island of the archipelago of the same name (Miyako Islands), which is located to the east of Taiwan, and administratively is part of the Okinawa prefecture. Other islands of the Miyako archipelago are Irabu, Minna, Tarama, Kurima, Ikema, Ogami, Shimoji. Together with the Yaeyama Islands (see Ishigaki), the Miyako Islands are part of the Sakishima Islands, in their turn belonging to the southern Ryukyus. The latitude of these islands is very low: a bit to the north of the Tropic of Cancer. Near the islands is a coral reef.
Here are the average temperatures.
Average temperatures - Miyakojima

Miyakojima	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Miyakojima	J	F	M	A	M	J	J	A	S	O	N	D
Min (°C)	16	16	18	20	23	25	27	26	25	24	21	18
Max (°C)	20	21	23	25	28	30	32	31	30	28	25	22
Min (°F)	61	61	64	68	73	77	81	79	77	75	70	64
Max (°F)	68	70	73	77	82	86	90	88	86	82	77	72

Although the winter is very mild, the sky is often cloudy, and periods of bad weather, with wind and rain, are quite common. Every now and then, especially in January, there can be very cool days, with highs around 16 °C (61 °F) or less, and lows around 10 °C (50 °F) or less.
The long summer is muggy, with fairly frequent, and sometimes abundant rains. The first part of the rainy season, called the plum rains (Baiu), begins one month earlier than in the main islands of Japan, so it occurs in May and June, however, between a shower and the other, the sun can come out, especially in June. In July there is a relative pause, so that the rains decrease, and sunshine becomes pretty frequent.
Here are the average daily sunshine hours.
Sunshine - Miyakojima

Miyakojima	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Miyakojima	J	F	M	A	M	J	J	A	S	O	N	D
Sun (hours)	3	3	4	4	5	6	8	7	6	5	4	3

In the second part of summer (August, September and early October), the rains increase again, but the sunshine amount remains generally decent, at least until September. If all goes well, a week can pass without rain, otherwise there may be periods of bad weather, or even typhoons.
In fact, from June to October, with a peak from August to early October, Miyako can be affected by typhoons, the tropical cyclones of Southeast Asia, which can bring strong winds and torrential rains.
Here is the average precipitation.
Average precipitation - Miyakojima

Miyakojima	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Year
Miyakojima	J	F	M	A	M	J	J	A	S	O	N	D	Y
Prec. (mm)	130	140	140	160	210	185	130	265	230	155	145	130	2020
Prec. (in)	5.1	5.5	5.5	6.3	8.3	7.3	5.1	10.4	9.1	6.1	5.7	5.1	79.5
Days	19	17	18	16	18	18	17	19	17	17	18	19	213

The sea in Miyako is never cold, in fact the temperature reaches a minimum of 23 °C (73 °F) in January and February, so if you want you can try to swim also in winter, while it gets very warm in summer.
Sea temperature - Miyakojima

Miyakojima	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Miyakojima	J	F	M	A	M	J	J	A	S	O	N	D
Sea (°C)	23	23	24	25	26	28	29	29	29	28	26	25
Sea (°F)	73	73	75	77	79	82	84	84	84	82	79	77