The following accommodation is an example of mid-budget price and great to share with other people. All speak English so you can book direct.
COTTAGE MORINOKOKAGEコテージ森のこかげ
Clean, modern wooden cabins with air conditioning, a veranda and a hammock. We’ve stayed in two different cabins and had a great night’s sleep. Barbecue facilities and a reserved bath house. The owner speaks good English and booking is easy. Location: Funayuki (See Google maps)
SHIKINOYADO ONOAIDA四季の宿 尾之間
This family-run minshuku offers a range of accommodation from rooms with balconies to large condos. We stayed in the biggest condo which was giant and comfortably sleeps up to 10 guests. It also has a barbecue area and the owner speaks English. Follow the link and book direct. Location: Onoaida (See Google maps)
YAKUSHIMA COTTAGE MORI NO FAIRY屋久島 コテージ 森のフェアリー
Wooden cabins in a row with balconies facing the sea. We stayed in two adjoining cabins and the owners have put in a lot of effort to make guests feel welcome. Follow the link and you can book direct on their English website. Location: Mugio (See Google maps)
For more information about Yakushima accommodation check out the one and only Yakumonkey Guide to Yakushima