The Ghosts of Cougar Island by Peggy Parish, 1986.
This book picks up soon after the previous book in the series ends.
The summer is almost over, and soon, the Roberts children will have to leave Pirate Island. Their grandfather tells them the story of nearby Cougar Island. The members of the Cougar family are all deceased, but the last member of the family said that anyone who trespassed on the island would be haunted by the ghosts of the Cougar family who are buried on the island. Although no one lives there now, some people have seen lights out on the island at midnight. The children’s grandfather even tried to go there once when he was young but turned back when he heard terrible moans. Liza, Bill, and Jed decide that they can’t possibly go home without trying to investigate this haunted island!
Strange things are happening on Pirate Island, too. Someone has been stealing food from Hermit Dan, but someone has also weeded his garden. On the one hand, he appreciates the help, but he can’t understand the thefts.
The children’s grandfather borrows a canoe for them, and the three of them take a trip out to the island. Sure enough, they encounter the terrible moans and a horrifying sound like the rattle of bones. Hermit Dan later offers them an explanation that helps set them at ease, but he can’t explain every mystery. Another visit to the island answers some of the children’s questions and leaves them with others, and a terrifying time in the old abandoned Cougar mansion convinces them of one thing: There is still someone on Cougar Island who shouldn’t be there. Someone who ate the lunch the children left behind earlier. Someone who lights candles at night in the old abandoned Cougar mansion. Someone who may even be responsible for the thefts on Pirate Island.